--- a/dictionary/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/dictionary/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -2,7 +2,7 @@
>
<html><head>
- <title>PROV Dictionary</title>
+ <title>PROV-Dictionary: Modeling Provenance for Dictionary Data Structures</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link rel="http://www.w3.org/ns/prov#has_provenance" href="http://www.w3.org/2011/prov/provenance/prov-dictionary"/>
@@ -618,7 +618,7 @@
};
var respecConfig = {
// specification status (e.g. WD, LCWD, NOTE, etc.). If in doubt use ED.
- specStatus: "ED", //WD-NOTE
+ specStatus: "NOTE", //WD-NOTE
// the specification's short name, as in http://www.w3.org/TR/short-name/
shortName: "prov-dictionary",
@@ -629,7 +629,7 @@
// if you wish the publication date to be other than today, set this
- //publishDate: "2013-03-12",
+ publishDate: "2013-04-30",
// if the specification's copyright date is a range of years, specify
// the start date here:
@@ -637,11 +637,11 @@
// if there is a previously published draft, uncomment this and set its YYYY-MM-DD date
// and its maturity status
- //previousPublishDate: "2012-07-24",
- //previousMaturity: "ED",
+ previousPublishDate: "2013-03-12",
+ previousMaturity: "FPWD",
// if there a publicly available Editor's Draft, this is the link
- edDraftURI: "http://dvcs.w3.org/hg/prov/raw-file/default/dictionary/Overview.html",
+ //edDraftURI: "http://dvcs.w3.org/hg/prov/raw-file/default/dictionary/Overview.html",
// if this is a LCWD, uncomment and set the end of its review period
//lcEnd: "2012-09-18",
@@ -718,31 +718,31 @@
This document is part of the PROV family of documents, a set of documents defining various aspects that are necessary to achieve the vision of inter-operable
interchange of provenance information in heterogeneous environments such as the Web. These documents are listed below. Please consult the [[PROV-OVERVIEW]] for a guide to reading these documents.
<ul>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/">PROV-OVERVIEW</a> (To be published as Note), an overview of the PROV family of documents [[PROV-OVERVIEW]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">PROV-PRIMER</a> (To be published as Note), a primer for the PROV data model [[PROV-PRIMER]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> (Proposed Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [[PROV-O]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> (Proposed Recommendation), the PROV data model for provenance [[PROV-DM]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> (Proposed Recommendation), a notation for provenance aimed at human consumption [[PROV-N]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> (Proposed Recommendation), a set of constraints applying to the PROV data model [[PROV-CONSTRAINTS]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> (To be published as Note), an XML schema for the PROV data model [[PROV-XML]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">PROV-AQ</a> (To be published as Note), the mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">PROV-DICTIONARY</a> (To be published as Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> (To be published as Note) provides a mapping between PROV and Dublic Core Terms [[PROV-DC]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> (To be published as Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> (To be published as Note) introduces a mechanism to link across bundles (this document).</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-overview-20130430/">PROV-OVERVIEW</a> (Note), an overview of the PROV family of documents [[PROV-OVERVIEW]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-primer-20130430/">PROV-PRIMER</a> (Note), a primer for the PROV data model [[PROV-PRIMER]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-o-20130430/">PROV-O</a> (Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of the PROV data model to RDF [[PROV-O]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/">PROV-DM</a> (Recommendation), the PROV data model for provenance [[PROV-DM]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-n-20130430/">PROV-N</a> (Recommendation), a notation for provenance aimed at human consumption [[PROV-N]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/">PROV-CONSTRAINTS</a> (Recommendation), a set of constraints applying to the PROV data model [[PROV-CONSTRAINTS]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs (this document);</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [[PROV-DC]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
</ul>
+<h4>Implementations Encouraged</h4>
+<p>
+The Provenance Working Group encourages implementation of the material defined in this document.
+ Although work on this document by the Provenance Working Group is complete,
+errors may be recorded in the <a href="http://www.w3.org/2011/prov/errata.html">errata</a> or and these may be addressed in future revisions.
+</p>
+
+<h4>Please Send Comments</h4>
+
</section>
-
-
-
-
-
-
-
-
-
<section id="introduction">
<h2>Introduction</h2>
@@ -770,7 +770,7 @@
<section id="dictionary-conceptual-definition">
<h2>Conceptual Definition of Dictionary</h2>
-<p>In this section a specific type of collection, as specified in [[PROV-DM]], is introduced. This new type of collection, Dictionary, is specified as follows.</p>
+<p>In this section a specific type of <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/#component6">collection</a>, as specified in [[PROV-DM]], is introduced. This new type of collection, Dictionary, is specified as follows.</p>
<span class="glossary-ref" data-ref="glossary-dictionary"></span>
@@ -779,14 +779,14 @@
This document provides a mechanism to assert the provenance for these types of data structures, in the most general way, as a collection of key-entity pairs, modified through insertions and deletions. Any more specialized structures can be modeled to some extent in terms of these key-entity pairs.
Here, we will discuss the provenance of dictionaries structured in terms of key-entity pairs. However, how this key-entity pair structure is translated to more specialized data structures, is beyond the scope of this document.</p>
-<p>In this document, a dictionary is viewed as a snapshot of a data structure with key-entity pairs, following a sequence of state-changing insertion and removal operations. These operations result in new snapshots, each snapshot forming a distinct and identifiable dictionary entity. Thus, when the structure of a dictionary changes (through insertions or removals), a new dictionary entity is defined, whereas the older dictionary entity remains the same.</p>
+<p>In this document, a dictionary is viewed as a snapshot of a data structure with key-entity pairs, following a sequence of state-changing insertion and removal operations. These operations result in new snapshots, each snapshot forming a distinct and identifiable dictionary entity. Thus, when the structure of a dictionary changes (through insertions or removals), a new dictionary entity is defined, whereas the older dictionary entity remains the same. The concepts defined in this document can be used to specify the differences between these dictionary entities.</p>
<!--
<span class="glossary-ref" data-ref="glossary-empty-dictionary"></span>
-->
-<p>Following the earlier definitions for generic collections, PROV-Dictionary defines the following types related to dictionaries:</p>
+<p>Following the <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/#term-collection">definition of prov:Collection</a>, PROV-Dictionary defines the following types related to dictionaries:</p>
<ul>
<li> <span class="name">prov:Dictionary</span> is a subtype of <span class="name">prov:Collection</span>. It denotes an entity of type dictionary, i.e. an entity that can participate in relations that involve dictionaries and their member entities;</li>
@@ -794,7 +794,7 @@
<li><span class="name">prov:EmptyDictionary</span> is a subtype of both <span class="name">prov:EmptyCollection</span> and <span class="name">prov:Dictionary</span>. It denotes an empty dictionary.</li>
</ul>
-<p>Note that the complete content of a dictionary is unknown unless it can be traced back to an empty dictionary through a series of insertions and removals. If an asserter wants to explicitly state that a dictionary is empty, it is recommended that the <span class="name">prov:type</span> <span class="name">prov:EmptyCollection</span> is used.
+<p>Note that the complete content of a dictionary is unknown unless it can be traced back to an empty dictionary through a series of insertions and removals. If an asserter wants to explicitly state that a dictionary is empty, it is recommended that the <span class="name">prov:type</span> <span class="name">prov:EmptyDictionary</span> is used.
<div class="anexample">
<pre class="codeexample">
@@ -827,7 +827,7 @@
<div class="anexample">
<pre class="codeexample">
-entity(d, [prov:type='prov:Dictionary' ]) // d1 is a dictionary, with (so far) unknown content
+entity(d, [prov:type='prov:Dictionary' ]) // d is a dictionary, with (so far) unknown content
entity(e1)
entity(e2)
@@ -866,10 +866,8 @@
<p>
An Insertion relation <span class="name">prov:derivedByInsertionFrom(id; d2, d1, {(key_1, e_1), ..., (key_n, e_n)})</span> states that <span class="name">d2</span> is the dictionary
-following the insertion of pairs <span class="name">(key_1, e_1)</span>, ..., <span class="name">(key_n, e_n)</span> into dictionary <span class="name">d1</span>.
-Note that insertion and the specified key-entity-set are considered to be complete. This means that we assume that no unknown keys were inserted in or removed from a dictionary after an insertion. This is formalized in <a href="#insertion-removal-membership-inference">Inference D8</a>.</p>
-
-
+following the insertion of key-entity pairs <span class="name">(key_1, e_1)</span>, ..., <span class="name">(key_n, e_n)</span> into dictionary <span class="name">d1</span>. In other words, the set of key-entity pairs <span class="name">{(key_1, e_1), ...,(key_n, e_n)}</span> is to be seen as the difference between <span class="name">d1</span> and <span class="name">d2</span>.
+Note that this key-entity-set is considered to be complete. This means that we assume that no unknown keys were inserted in or removed from a dictionary derived by an insertion relation. This is formalized in <a href="#insertion-removal-membership-inference">Inference D8</a>.</p>
<div class="anexample">
<pre class="codeexample">
@@ -934,8 +932,8 @@
</ul>
</div>
-<p>A Removal relation <span class="name">prov:derivedByRemovalFrom(id; d2,d1, {key_1, ..., key_n})</span> states that <span class="name">d2</span> is the dictionary following the removal of the set of pairs corresponding to keys <span class="name">key_1...key_n</span> from <span class="name">d1</span>. If a key that is not present in the dictionary is removed, the dictionary remains unchanged.
- Note that removal and the specified key-set are considered to be complete. This means that we assume that no unknown keys were inserted in or removed from a dictionary after a removal. This is formalized in <a href="#insertion-removal-membership-inference">Inference D8</a>.
+<p>A Removal relation <span class="name">prov:derivedByRemovalFrom(id; d2,d1, {key_1, ..., key_n})</span> states that <span class="name">d2</span> is the dictionary following the removal of the set of pairs corresponding to keys <span class="name">key_1...key_n</span> from <span class="name">d1</span>.
+ In other words, the key-set <span class="name">{key_1,...,key_n}</span> is to be seen as the difference in keys and corresponding entities between <span class="name">d1</span> and <span class="name">d2</span>. Note that this key-set is considered to be complete. This means that we assume that no unknown keys were inserted in or removed from a dictionary derived by a removal relation. This is formalized in <a href="#insertion-removal-membership-inference">Inference D8</a>.
</p>
<div class="anexample">
@@ -962,7 +960,7 @@
<li><span class="name">d3</span> was the dictionary <span class="name">{ ("k2", e2) }</span> </li>
<li><span class="name">d4</span> was the dictionary <span class="name">{ ("k2", e2) }</span> </li>
</ul>
-Note that "k1" was not present in d3, and thus its removal to obtain d4 did not change the contents of the dictionary.
+Note that there is no constraint stating that removed keys had to be present in the original dictionary. For example, "k1" was not present in d3, and thus its removal to obtain d4 did not change the contents of the dictionary.
</div>
</section> <!-- end removal -->
@@ -972,14 +970,11 @@
<section id="dictionary-notation">
<h2>PROV-N Notation of Dictionary Concepts</h2>
The notation used for dictionaries in this document extends the standard PROV-N according to the principles described in <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#extensibility">the PROV-N extensibility chapter</a>.
-However, because dictionaries are defined in the same namespace as the rest of PROV-N, the terms in this document do not have a non-empty prefix. For the remainder of this document, we will assume that the default namespace http://www.w3.org/ns/prov# is used, and thus, no prefix is specified for the terms associated with dictionaries.
-<div class="note">Note that the use of a non-empty prefix for extensions of PROV-N is technically not valid. The terms used in this document can be made valid by the addition of a prefix "prov:" to all PROV-Dictionary terms. However, this would greatly reduce the readability of this document.
- The Working Group is currently discussing how to address this issue before the next Working Draft of this document.</div>
-The [<a href="http://dvcs.w3.org/hg/prov/raw-file/default/dictionary/prov-dictionary-grammar.txt">Grammar for PROV-Dictionary</a>] is available for download.
+The [<a href="prov-dictionary-grammar.txt">Grammar for PROV-Dictionary</a>] is available for download.
<section id="expression-dictionary">
<h3>Dictionary and EmptyDictionary Expression</h3>
- PROV-Dictionary provides no dedicated syntax for Collection and EmptyCollection. Dictionaries are declared in <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#expression-collection">the same way</a> as Collections. A Dictionary or an EmptyDictionary MUST be expressed as an
+ PROV-Dictionary provides no dedicated syntax for Dictionary and EmptyDictionary. Dictionaries are declared in <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#expression-collection">the same way</a> as Collections. A Dictionary or an EmptyDictionary MUST be expressed as an
<code class="content"><a class="grammarRef" href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-entityExpression">entityExpression</a></code> with attribute
<span id="provn-type-Dictionary"><code>prov:type='prov:Dictionary'</code></span>, or
<span id="provn-type-EmptyDictionary"><code>prov:type='prov:EmptyDictionary'</code></span>, respectively.
@@ -992,22 +987,26 @@
</div>
</section>
<section id="expression-dictionary-membership">
-<h3>Membership</h3>
-
-<div class="grammar">
- <span class="nonterminal">membershipExpression</span> ::=
-<span class="name">prov:hadDictionaryMember</span>
- <span class="name">(</span>
-<span class="nonterminal">dIdentifier</span>
- <span class="name">,</span>
- <span class="nonterminal">eIdentifier</span>
- <span class="name">,</span>
- <span class="nonterminal">key</span>
- <span class="name">)</span>
- <br>
-</div>
-
-<p>The following table summarizes how each constituent of a PROV-DM Membership maps to a non-terminal.</p>
+<h3>Dictionary Membership</h3>
+<table class="grammar">
+<tbody class="prod">
+<tr style="vertical-align: baseline; ">
+<td><a id="prod-dictionaryMembershipExpression" data-name="prod-dictionaryMembershipExpression"></a>[<span class="prodNo">1</span>] </td>
+<td><code class="production prod">dictionaryMembershipExpression</code></td>
+<td> ::= </td>
+<td><code class="content">"prov:hadDictionaryMember" "(" <span class="prod"><a class="grammarRef" href="#prod-dIdentifier">dIdentifier</a></span>
+ ","
+ <span class="prod"><a class="grammarRef" href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-eIdentifier">eIdentifier</a></span>
+ ","
+ <span class="prod"><a class="grammarRef" href="#prod-key">key</a></span>
+ ")"
+ </code>
+ </td>
+</tr>
+</tbody>
+</table>
+
+<p>The following table summarizes how each constituent of a PROV-Dictionary Membership maps to a non-terminal.</p>
<div style="text-align: left; ">
<table class="thinborder" style="margin-left: auto; margin-right: auto;">
@@ -1038,23 +1037,28 @@
</section> <!-- membership -->
<section id="expression-dictionary-insertion">
<h3>Insertion</h3>
-<div class="grammar">
- <span class="nonterminal">derivationByInsertionFromExpression</span> ::=
-<span class="name">prov:derivedByInsertionFrom</span>
- <span class="name">(</span>
- <span class="optional"><span class="nonterminal">optionalIdentifier</span>
- <span class="name">;</span></span>
-<span class="nonterminal">dIdentifier</span>
- <span class="name">,</span>
-<span class="nonterminal">dIdentifier</span>
- <span class="name">,</span>
- <span class="name">{</span>
- <span class="nonterminal">keyEntityPairs</span>
- <span class="name">}</span>
- <span class="name">,</span>
-<span class="nonterminal">optionalAttributeValuePairs</span>
- <span class="name">)</span>
-</div>
+<table class="grammar">
+<tbody class="prod">
+ <tr style="vertical-align: baseline; ">
+<td><a id="prod-derivationByInsertionFromExpression" data-name="prod-derivationByInsertionFromExpression"></a>[<span class="prodNo">2</span>] </td>
+<td><code class="production prod">derivationByInsertionFromExpression</code></td>
+<td> ::= </td>
+<td><code class="content">"prov:derivedByInsertionFrom" "("
+ (<span class="prod"><a class="grammarRef" href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-optionalIdentifier">optionalIdentifier</a></span>
+ ";")?
+ <span class="prod"><a class="grammarRef" href="#prod-dIdentifier">dIdentifier</a></span>
+ ","
+ <span class="prod"><a class="grammarRef" href="#prod-dIdentifier">dIdentifier</a></span>
+ "," "{"
+ <span class="prod"><a class="grammarRef" href="#prod-keyEntityPairs">keyEntityPairs</a></span>
+ "}"
+ <span class="prod"><a class="grammarRef" href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-optionalAttributeValuePairs">optionalAttributeValuePairs</a></span>
+ ")"
+ </code>
+ </td>
+</tr>
+</tbody>
+</table>
<p>The following table summarizes how each constituent of a PROV-Dictionary Insertion maps to a non-terminal.</p>
@@ -1101,24 +1105,29 @@
</section> <!-- Insertion -->
<section id="expression-dictionary-removal">
<h3>Removal</h3>
-<div class="grammar">
- <span class="nonterminal">derivationByRemovalFromExpression</span> ::=
-<span class="name">prov:derivedByRemovalFrom</span>
- <span class="name">(</span>
- <span class="optional"><span class="nonterminal">optionalIdentifier</span>
- <span class="name">;</span></span>
-<span class="nonterminal">dIdentifier</span>
- <span class="name">,</span>
-<span class="nonterminal">dIdentifier</span>
- <span class="name">,</span>
- <span class="name">{</span>
- <span class="nonterminal">keySet</span>
- <span class="name">}</span>
- <span class="name">,</span>
-<span class="nonterminal">optionalAttributeValuePairs</span>
- <span class="name">)</span>
- <br>
-</div>
+<table class="grammar">
+<tbody class="prod">
+ <tr style="vertical-align: baseline; ">
+<td><a id="prod-derivationByRemovalFromExpression" data-name="prod-derivationByRemovalFromExpression"></a>[<span class="prodNo">3</span>] </td>
+<td><code class="production prod">derivationByRemovalFromExpression</code></td>
+<td> ::= </td>
+<td><code class="content">"prov:derivedByRemovalFrom" "("
+ (<span class="prod"><a class="grammarRef" href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-optionalIdentifier">optionalIdentifier</a></span>
+ ";")?
+ <span class="prod"><a class="grammarRef" href="#prod-dIdentifier">dIdentifier</a></span>
+ ","
+ <span class="prod"><a class="grammarRef" href="#prod-dIdentifier">dIdentifier</a></span>
+ "," "{"
+ <span class="prod"><a class="grammarRef" href="#prod-keySet">keySet</a></span>
+ "}"
+ <span class="prod"><a class="grammarRef" href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-optionalAttributeValuePairs">optionalAttributeValuePairs</a></span>
+ ")"
+ </code>
+ </td>
+</tr>
+</tbody>
+</table>
+
<p>The following table summarizes how each constituent of a PROV-Dictionary Removal maps to a non-terminal.</p>
<div style="text-align: left; ">
@@ -1148,7 +1157,7 @@
</pre>
<p> Here
<span class="name">id</span> is the optional removal identifier,
- <span class="name">d1</span> is the identifier for the collection after the removal,
+ <span class="name">d3</span> is the identifier for the collection after the removal,
<span class="name">d</span> is the identifier for the collection before the removal,
<span class="name"> {"k1", "k2"}</span> is the set of keys that have been removed from
<span class="name">d</span>,
@@ -1169,23 +1178,52 @@
<h3>Other expressions</h3>
For the notation of dictionaries, we used some new non-terminals. We provide their production rules here.
-<div class="grammar">
-<p id="prod-dIdentifier"><span class="nonterminal">dIdentifier</span> ::=
- <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-identifier" class="nonterminal">identifier</a> </p>
-
-<p id="prod-key"><span class="nonterminal">key</span> ::=
- <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-literal" class="nonterminal">literal</a> </p>
-
- <p id="prod-keyEntityPairs"><span class="nonterminal">keyEntityPairs</span> ::=
- <a href="#prod-keyEntityPair" class="nonterminal">keyEntityPair</a> <span class="star"><span class="name">,</span> <a href="#prod-keyEntityPair" class="nonterminal">keyEntityPair</a></span> </p>
-
- <p id="prod-keyEntityPair"><span class="nonterminal">keyEntityPair</span> ::=
- <span class="name">(</span> <a href="#prod-key" class="nonterminal">key</a> <span class="name">,</span> <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-eIdentifier" class="nonterminal">eIdentifier</a> <span class="name">)</span> </p>
-
- <p id="prod-keySet"><span class="nonterminal">keySet</span> ::=
- <a href="#prod-key" class="nonterminal">key</a> <span class="star"><span class="name">,</span> <a href="#prod-key" class="nonterminal">key</a></span> </p>
-
-</div>
+<table class="grammar">
+<tbody class="prod">
+ <tr style="vertical-align: baseline; ">
+ <td><a id="prod-dIdentifier" data-name="prod-dIdentifier"></a>[<span class="prodNo">4</span>] </td>
+ <td><code class="production prod">dIdentifier</code></td>
+ <td> ::= </td>
+ <td><code class="content"><span class="prod"><a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-identifier" class="nonterminal">identifier</a></span>
+ </code></td>
+ </tr>
+
+ <tr style="vertical-align: baseline; ">
+ <td><a id="prod-key" data-name="prod-key"></a>[<span class="prodNo">5</span>] </td>
+ <td><code class="production prod">key</code></td>
+ <td> ::= </td>
+ <td><code class="content"><span class="prod"><a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-literal" class="nonterminal">literal</a></span> </code>
+ </td>
+ </tr>
+
+ <tr style="vertical-align: baseline; ">
+ <td><a id="prod-keyEntityPairs" data-name="prod-keyEntityPairs"></a>[<span class="prodNo">6</span>] </td>
+ <td><code class="production prod">keyEntityPairs</code></td>
+ <td> ::= </td>
+ <td><code class="content"><span class="prod"><a href="#prod-keyEntityPair" class="nonterminal">keyEntityPair</a></span>
+ ("," <span class="prod"><a href="#prod-keyEntityPair" class="nonterminal">keyEntityPair</a></span>)*</code>
+ </td>
+ </tr>
+
+ <tr style="vertical-align: baseline; ">
+ <td><a id="prod-keyEntityPair" data-name="prod-keyEntityPair"></a>[<span class="prodNo">7</span>] </td>
+ <td><code class="production prod">keyEntityPair</code></td>
+ <td> ::= </td>
+ <td><code class="content">"(" <span class="prod"><a href="#prod-key" class="nonterminal">key</a> </span>
+ "," <span class="prod"><a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/#prod-eIdentifier" class="nonterminal">eIdentifier</a></span> ")"</code>
+ </td>
+ </tr>
+
+ <tr style="vertical-align: baseline; ">
+ <td><a id="prod-keySet" data-name="prod-keySet"></a>[<span class="prodNo">8</span>] </td>
+ <td><code class="production prod">keySet</code></td>
+ <td> ::= </td>
+ <td><code class="content"><span class="prod"><a href="#prod-key" class="nonterminal">key</a></span>
+ ("," <span class="prod"><a href="#prod-key" class="nonterminal">key</a></span>)*</code>
+ </td>
+ </tr>
+</tbody>
+</table>
</section> <!-- other -->
</section>
@@ -1193,9 +1231,8 @@
<section id="dictionary-ontological-definition">
<h2>PROV-O Representation of Dictionary</h2>
<p>In this section, the ontological definition of <code>prov:Dictionary</code> is given, in order to extend [[PROV-O]] with dictionaries. For more information on the terminology, syntax and conventions used in this section, we refer to [[PROV-O]].</p>
-<p>The classes and properties defined in this document will be included in the default namespace of PROV.
- Users of the ontology have the option of importing <code><http://www.w3.org/ns/prov#></code>, which includes all extensions, including PROV-Dictionary, or if they wish to have only [[PROV-O]] terms, they can import <code><http://www.w3.org/ns/prov-o#></code>. Similarly, <code><http://www.w3.org/ns/prov-dictionary#></code> holds only the PROV-Dictionary terms.
-The [<a href="https://dvcs.w3.org/hg/prov/raw-file/default/dictionary/prov-dictionary.owl">OWL file for PROV-Dictionary</a>] is available for download. (Note that this file is unfinished at the time of this working draft, and may be subject to change.)</p>
+<p>The classes and properties defined in this document are included in the default namespace of PROV.
+ Users of the ontology have the option of importing <code><http://www.w3.org/ns/prov#></code>, which includes all extensions, including PROV-Dictionary. Additionally, the [<a href="prov-dictionary.owl">OWL file for PROV-Dictionary</a>] is available for download.</p>
<p> A <code><a class="qname"
href='#Dictionary'>prov:Dictionary</a></code> is a <code
@@ -1363,12 +1400,12 @@
<div id="Dictionary" class="entity">
<h3>
Class: <a href="#Dictionary"><span class="dotted" title="http://www.w3.org/ns/prov#Dictionary">prov:Dictionary</span></a>
- <span class="backlink">
+ </h3>
+ <span class="backlink">
back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
</span>
- </h3>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#Dictionary</p>
- <div class="definition"><p>A dictionary is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the dictionary.</p>
+ <div class="definition"><p>A dictionary is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be members of the dictionary.</p>
</div>
<div class="example">
@@ -1427,12 +1464,13 @@
<div id="EmptyDictionary" class="entity">
<h3>
Class: <a href="#EmptyDictionary"><span class="dotted" title="http://www.w3.org/ns/prov#EmptyDictionary">prov:EmptyDictionary</span></a>
- <span class="backlink">
+ </h3>
+ <span class="backlink">
back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
- </span>
- </h3>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#EmptyDictionary</p>
-
+ <div class="definition">
+<p>An empty dictionary is a dictionary that has no members.</p></div>
<div class="example">
<strong>Example</strong>
<pre>@prefix prov: <http://www.w3.org/ns/prov#> .
@@ -1447,7 +1485,7 @@
</div>
<dl class="description">
- <dd class="comment"><p>An empty dictionary (i.e. has no members).</p>
+ <dd class="comment">
</dd>
<dt>is subclass of</dt>
@@ -1458,15 +1496,70 @@
</dl>
</div>
+ <div id="KeyEntityPair" class="entity">
+ <h3>
+ Class: <a href="#KeyEntityPair"><span class="dotted" title="http://www.w3.org/ns/prov#KeyEntityPair">prov:KeyEntityPair</span></a>
+ </h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
+ <p><strong>IRI:</strong>http://www.w3.org/ns/prov#KeyEntityPair</p>
+<div class="definition"><p>A key-entity pair. Part of a prov:Dictionary through prov:hadDictionaryMember. The key is any RDF Literal, the value is a prov:Entity.</p>
+ </div>
+ <div class="example">
+ <strong>Example</strong>
+ <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
+@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
+@prefix owl: <http://www.w3.org/2002/07/owl#> .
+@prefix prov: <http://www.w3.org/ns/prov#> .
+@prefix : <http://example.com/> .
+
+
+:our-baseball-team-field-positions
+ a prov:Dictionary,
+ :FieldPositions;
+ prov:hadDictionaryMember [
+ a prov:KeyEntityPair;
+ prov:pairKey "first-baseman"^^xsd:string;
+ prov:pairEntity :george;
+ ];
+ prov:hadDictionaryMember [
+ a prov:KeyEntityPair;
+ prov:pairKey "pitcher"^^xsd:string;
+ prov:pairEntity :carl;
+ ];
+.
+
+:george a prov:Entity .
+:carl a prov:Entity .
+</pre>
+ </div>
+
+ <dl class="description">
+ <dd class="comment"></dd>
+
+ <dt>described with properties</dt>
+ <dd>
+ <a title="http://www.w3.org/ns/prov#pairKey" href="#pairKey">prov:pairKey</a><sup class="type-dp" title="data property">dp</sup>
+ <a title="http://www.w3.org/ns/prov#pairEntity" href="#pairEntity">prov:pairEntity</a><sup class="type-op" title="object property">op</sup>
+ </dd>
+
+ <dt>in range of</dt>
+ <dd>
+ <a title="http://www.w3.org/ns/prov#hadDictionaryMember" href="#hadDictionaryMember">prov:hadDictionaryMember</a><sup class="type-op" title="object property">op</sup>
+ <a title="http://www.w3.org/ns/prov#insertedKeyEntityPair" href="#insertedKeyEntityPair">prov:insertedKeyEntityPair</a><sup class="type-op" title="object property">op</sup>
+ </dd>
+ </dl>
+ </div>
<div id="Insertion" class="entity">
<h3>
Class: <a href="#Insertion"><span class="dotted" title="http://www.w3.org/ns/prov#Insertion">prov:Insertion</span></a>
+ </h3>
<span class="backlink">
back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
</span>
- </h3>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#Insertion</p>
- <div class="definition"><p>Insertion is a derivation that transforms a dictionary into another, by insertion of one or more key-entity pairs.</p>
+ <div class="definition"><p>Insertion is a derivation that describes the transformation of a dictionary into another, by insertion of one or more key-entity pairs.</p>
</div>
<div class="example">
@@ -1499,8 +1592,7 @@
</div>
<dl class="description">
- <dd class="comment"><p>Insertion is a derivation that transforms a dictionary into another, by insertion of one or more key-entity pairs.</p>
- </dd>
+ <dd class="comment"></dd>
<dt>is subclass of</dt>
<dd>
@@ -1523,72 +1615,15 @@
</dd>
</dl>
</div>
-
- <div id="KeyEntityPair" class="entity">
+ <div id="Removal" class="entity">
<h3>
- Class: <a href="#KeyEntityPair"><span class="dotted" title="http://www.w3.org/ns/prov#KeyEntityPair">prov:KeyEntityPair</span></a>
+ Class: <a href="#Removal"><span class="dotted" title="http://www.w3.org/ns/prov#Removal">prov:Removal</span></a>
+ </h3>
<span class="backlink">
back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
</span>
- </h3>
- <p><strong>IRI:</strong>http://www.w3.org/ns/prov#KeyEntityPair</p>
-
- <div class="example">
- <strong>Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-
-:our-baseball-team-field-positions
- a prov:Dictionary,
- :FieldPositions;
- prov:hadDictionaryMember [
- a prov:KeyEntityPair;
- prov:pairKey "first-baseman"^^xsd:string;
- prov:pairEntity :george;
- ];
- prov:hadDictionaryMember [
- a prov:KeyEntityPair;
- prov:pairKey "pitcher"^^xsd:string;
- prov:pairEntity :carl;
- ];
-.
-
-:george a prov:Entity .
-:carl a prov:Entity .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>A key-entity pair. Part of a prov:Dictionary through prov:hadDictionaryMember. The key is any RDF Literal, the value is a prov:Entity.</p>
- </dd>
-
- <dt>described with properties</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#pairKey" href="#pairKey">prov:pairKey</a><sup class="type-dp" title="data property">dp</sup>
- <a title="http://www.w3.org/ns/prov#pairEntity" href="#pairEntity">prov:pairEntity</a><sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadDictionaryMember" href="#hadDictionaryMember">prov:hadDictionaryMember</a><sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#insertedKeyEntityPair" href="#insertedKeyEntityPair">prov:insertedKeyEntityPair</a><sup class="type-op" title="object property">op</sup>
- </dd>
- </dl>
- </div>
-
- <div id="Removal" class="entity">
- <h3>
- Class: <a href="#Removal"><span class="dotted" title="http://www.w3.org/ns/prov#Removal">prov:Removal</span></a>
- <span class="backlink">
- back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
- </span>
- </h3>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#Removal</p>
- <div class="definition"><p>Removal is a derivation that transforms a dictionary into another, by removing one or more key-entity pairs.</p>
+ <div class="definition"><p>Removal is a derivation that describes the transformation of a dictionary into another, by removing one or more keys.</p>
</div>
<div class="example">
@@ -1616,8 +1651,7 @@
</div>
<div>
<dl class="description">
- <dd class="comment"><p>Removal is a derivation that transforms a dictionary into another, by removing one or more key-entity pairs specified by <a title="http://www.w3.org/ns/prov#removedKey" href="#removedKey">prov:removedKey</a>.</p>
- </dd>
+ <dd class="comment"></dd>
<dt>is subclass of</dt>
<dd>
@@ -1652,8 +1686,12 @@
Property: <a href="#derivedByInsertionFrom"><span class="dotted" title="http://www.w3.org/ns/prov#derivedByInsertionFrom">prov:derivedByInsertionFrom</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#derivedByInsertionFrom</p>
-
+<div class="definition"><p>The dictionary was derived from the other by insertion. Can be qualified with prov:qualifiedInsertion, which shows details of the insertion, in particular the inserted key-entity pairs.</p>
+ </div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -1687,8 +1725,7 @@
</div>
<div class="description">
- <div class="comment"><p>The dictionary was derived from the other by insertion. prov:qualifiedInsertion shows details of the insertion, in particular the inserted key-entity pairs.</p>
- </div>
+ <div class="comment"></div>
<dl>
<dt>has super-properties</dt>
@@ -1739,8 +1776,12 @@
Property: <a href="#derivedByRemovalFrom"><span class="dotted" title="http://www.w3.org/ns/prov#derivedByRemovalFrom">prov:derivedByRemovalFrom</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#derivedByRemovalFrom</p>
-
+<div class="definition"><p>The dictionary was derived from the other by removal. Can be qualified with prov:qualifiedRemoval, which shows details of the removal, in particular the removed keys.</p>
+ </div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -1765,8 +1806,7 @@
</div>
<div class="description">
- <div class="comment"><p>The dictionary was derived from the other by removal. prov:qualifiedRemoval shows details of the removal, in particular the removed key-entity pairs.</p>
- </div>
+ <div class="comment"></div>
<dl>
<dt>has super-properties</dt>
@@ -1817,8 +1857,12 @@
Property: <a href="#dictionary"><span class="dotted" title="http://www.w3.org/ns/prov#dictionary">prov:dictionary</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#dictionary</p>
-
+ <div class="definition"><p>The property used by a prov:Insertion and prov:Removal to cite the prov:Dictionary that was prov:derivedByInsertionFrom or prov:derivedByRemovalFrom another dictionary. </p>
+ </div>
<div class="example">
<strong>Example</strong>
<pre>@prefix prov: <http://www.w3.org/ns/prov#> .
@@ -1845,8 +1889,7 @@
</div>
<div class="description">
- <div class="comment"><p>The property used by a prov:Insertion and prov:Removal to cite the prov:Dictionary that was prov:derivedByInsertionFrom or prov:derivedByRemovalFrom another dictionary. </p>
- </div>
+ <div class="comment"></div>
<dl>
<dt>has super-properties</dt>
@@ -1886,8 +1929,12 @@
Property: <a href="#insertedKeyEntityPair"><span class="dotted" title="http://www.w3.org/ns/prov#insertedKeyEntityPair">prov:insertedKeyEntityPair</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#insertedKeyEntityPair</p>
-
+<div class="definition"><p>An object property to refer to the prov:KeyEntityPair inserted into a prov:Dictionary.</p>
+ </div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -1918,7 +1965,7 @@
</div>
<div class="description">
- <div class="comment"><p>An object property to refer to the prov:KeyEntityPair inserted into a prov:Dictionary.</p>
+ <div class="comment">
</div>
<dl>
@@ -1949,8 +1996,12 @@
Property: <a href="#hadDictionaryMember"><span class="dotted" title="http://www.w3.org/ns/prov#hadDictionaryMember">prov:hadDictionaryMember</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#hadDictionaryMember</p>
-
+<div class="definition"><p>Describes the key-entity pair that was member of a prov:Dictionary. A dictionary can have multiple members.</p>
+ </div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -1979,7 +2030,7 @@
</div>
<div class="description">
- <div class="comment"><p>Describes the key-entity pair that was member of a prov:Dictionary. A dictionary can have multiple members.</p>
+ <div class="comment">
</div>
<dl>
@@ -2011,8 +2062,11 @@
Property: <a href="#pairKey"><span class="dotted" title="http://www.w3.org/ns/prov#pairKey">prov:pairKey</span></a><sup class="type-dp" title="data property">dp</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#pairKey</p>
-
+ <div class="definition"><p>The key of a prov:KeyEntityPair, which is an element of a prov:Dictionary.</p></div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -2041,7 +2095,7 @@
</div>
<div class="description">
- <div class="comment"><p>The key of a KeyEntityPair, which is an element of a prov:Dictionary.</p>
+ <div class="comment">
</div>
<p><strong>has characteristics</strong> <a href="http://www.w3.org/TR/owl2-syntax/#Functional_Object_Properties"> Functional</a> </p>
<dl>
@@ -2073,8 +2127,12 @@
Property: <a href="#pairEntity"><span class="dotted" title="http://www.w3.org/ns/prov#pairEntity">prov:pairEntity</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#pairEntity</p>
+ <div class="definition"><p>The entity of a prov:KeyEntityPair, which is an element of a prov:Dictionary.</p></div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -2103,8 +2161,6 @@
</div>
<div class="description">
- <div class="comment"><p>The value of a KeyEntityPair.</p>
- </div>
<p><strong>has characteristics</strong> <a href="http://www.w3.org/TR/owl2-syntax/#Functional_Object_Properties"> Functional</a> </p>
<dl>
@@ -2135,8 +2191,11 @@
Property: <a href="#qualifiedInsertion"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedInsertion">prov:qualifiedInsertion</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#qualifiedInsertion</p>
-
+ <div class="definition"><p>prov:qualifiedInsertion shows the details of an insertion, in particular the inserted key-entity pairs.</p></div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -2170,8 +2229,7 @@
</div>
<div class="description">
- <div class="comment"><p>The dictionary was derived from the other by insertion. prov:qualifiedInsertion shows details of the insertion, in particular the inserted key-entity pairs.</p>
- </div>
+ <div class="comment"></div>
<dl>
<dt>has super-properties</dt>
@@ -2215,8 +2273,12 @@
Property: <a href="#qualifiedRemoval"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedRemoval">prov:qualifiedRemoval</span></a><sup class="type-op" title="object property">op</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#qualifiedRemoval</p>
+ <div class="definition"><p>prov:qualifiedRemoval shows the details of a removal, in particular the removed keys.</p></div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -2284,8 +2346,11 @@
Property: <a href="#removedKey"><span class="dotted" title="http://www.w3.org/ns/prov#removedKey">prov:removedKey</span></a><sup class="type-dp" title="data property">dp</sup>
</h3>
+ <span class="backlink">
+ back to <a href="#prov-dictionary-owl-terms-at-a-glance">overview</a>
+ </span>
<p><strong>IRI:</strong>http://www.w3.org/ns/prov#removedKey</p>
-
+ <div class="definition"><p>The key removed in a Removal.</p></div>
<div class="example">
<strong>Example</strong>
<pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@@ -2311,7 +2376,7 @@
</div>
<div class="description">
- <div class="comment"><p>The key removed in a Removal.</p>
+ <div class="comment">
</div>
<dl>
@@ -2344,12 +2409,11 @@
<section id="dictionary-xml-schema">
<h2>PROV-XML Representation of Dictionary</h2>
This section details how to describe dictionaries with
-the [[PROV-XML]] serialization. The [<a href="http://dvcs.w3.org/hg/prov/raw-file/default/xml/schema/prov-dictionary.xsd">XML schema for PROV-Dictionary</a>] is available for download.
-<div class="note">The Working Group is currently discussing the best way of disseminating the XML Schema for PROV-DM and its extensions. For now, we recommend importing both the [<a href="https://dvcs.w3.org/hg/prov/raw-file/default/xml/prov-xml.html#prov-xml-schema">PROV-XML Schema</a>] and the [<a href="https://dvcs.w3.org/hg/prov/raw-file/default/xml/schema/prov-dictionary.xsd">XML schema for PROV-Dictionary</a>].</div>
+the [[PROV-XML]] serialization. The [<a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/schema/prov-dictionary.xsd">XML schema for PROV-Dictionary</a>] is available for download, and includes <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/schema/prov-core.xsd">prov-core.xsd</a>, the core schema of PROV. Alternatively, the default schema, <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/schema/prov.xsd">prov.xsd</a> can be used, which imports <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/schema/prov-core.xsd">prov-core.xsd</a> and all extension schemas developed by the Working Group.
<section id="term-Dictionary">
<h3>Dictionary</h3>
<div class="glossary-ref" data-ref="glossary-dictionary"></div>
-<p>To specialize an Entity as a Dictionary, include a <code>prov:type</code> with the value "prov:Dictionary".</p>
+<p>To specialize an Entity as a prov:Dictionary or prov:EmptyDictionary, the element <code><prov:dictionary></code> or <code><prov:emptyDictionary></code> is used, respectively.<p>
<pre class="schema-type">
<xs:complexType xmlns:xs="http://www.w3.org/2001/XMLSchema" name="Dictionary" >
<xs:complexContent>
@@ -2357,6 +2421,7 @@
</xs:complexContent>
</xs:complexType>
</pre>
+<p>Usage in XML:<p>
<pre class="schema-usage">
<xs:element name="dictionary" type="prov:Dictionary" substitutionGroup="prov:internalElement" />
</pre>
@@ -2368,9 +2433,11 @@
</xs:complexContent>
</xs:complexType>
</pre>
+<p>Usage in XML:<p>
<pre class="schema-usage">
<xs:element name="emptyDictionary" type="prov:EmptyDictionary" substitutionGroup="prov:internalElement" />
</pre>
+
<pre class="example">
<prov:document
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
@@ -2379,14 +2446,10 @@
xmlns:ex="http://example.com/ns/ex#">
<!-- d0 is an empty dictionary -->
- <b><prov:entity prov:id="d0">
- <prov:type xsi:type="xsd:QName">prov:EmptyDictionary</prov:type>
- </prov:entity></b>
+ <b><prov:emptyDictionary prov:id="d0" /></b>
<!-- d1 is a dictionary, with (so far) unknown content -->
- <b><prov:entity prov:id="d1">
- <prov:type xsi:type="xsd:QName">prov:Dictionary</prov:type>
- </prov:entity></b>
+ <b><prov:dictionary prov:id="d1" /></b>
</prov:document>
</pre>
@@ -2400,8 +2463,8 @@
<pre class="schema-type">
<xs:complexType xmlns:xs="http://www.w3.org/2001/XMLSchema" name="KeyEntityPair" >
<xs:sequence>
+ <xs:element name="key" type="xs:anySimpleType" />
<xs:element name="entity" type="prov:IDRef" />
- <xs:element name="key" type="xs:anySimpleType" />
</xs:sequence>
</xs:complexType>
</pre>
@@ -2419,13 +2482,13 @@
<prov:entity prov:id="e1"/>
<b><prov:keyEntityPair>
+ <prov:key>k0</prov:key>
<prov:entity prov:ref="e0"/>
- <prov:key>k0</prov:key>
</prov:keyEntityPair>
<prov:keyEntityPair>
+ <prov:key>k1</prov:key>
<prov:entity prov:ref="e1"/>
- <prov:key>k1</prov:key>
</prov:keyEntityPair></b>
</prov:document>
</pre>
@@ -2439,7 +2502,7 @@
<xs:complexType xmlns:xs="http://www.w3.org/2001/XMLSchema" name="DictionaryMembership">
<xs:sequence>
<xs:element name="dictionary" type="prov:IDRef"/>
- <xs:element name="keyEntityPair type="prov:KeyEntityPair" maxOccurs="unbounded"/>
+ <xs:element name="keyEntityPair type="prov:KeyEntityPair" minOccurs=1 maxOccurs="unbounded"/>
</xs:sequence>
</xs:complexType>
</pre>
@@ -2456,9 +2519,7 @@
<prov:entity prov:id="e1"/>
<prov:entity prov:id="e2"/>
- <prov:entity prov:id="d">
- <prov:type xsi:type="xsd:QName">prov:Dictionary</prov:type>
- </prov:entity>
+ <prov:dictionary prov:id="d" />
<b><prov:hadDictionaryMember>
<prov:dictionary prov:ref="d"/>
@@ -2489,7 +2550,7 @@
<xs:sequence>
<xs:element name="newDictionary" type="prov:IDRef"/>
<xs:element name="oldDictionary" type="prov:IDRef"/>
- <xs:element name="keyEntityPair type="prov:KeyEntityPair" maxOccurs="unbounded"/>
+ <xs:element name="keyEntityPair type="prov:KeyEntityPair" minOccurs=1 maxOccurs="unbounded"/>
<xs:element ref="prov:label" minOccurs="0" maxOccurs="unbounded"/>
<xs:element ref="prov:type" minOccurs="0" maxOccurs="unbounded"/>
<xs:any namespace="##other" processContents="lax" minOccurs="0" maxOccurs="unbounded"/>
@@ -2510,13 +2571,9 @@
<prov:entity prov:id="e1"/>
<prov:entity prov:id="e2"/>
- <prov:entity prov:id="d1">
- <prov:type xsi:type="xsd:QName">prov:Dictionary</prov:type>
- </prov:entity>
+ <prov:dictionary prov:id="d1" />
- <prov:entity prov:id="d2">
- <prov:type xsi:type="xsd:QName">prov:Dictionary</prov:type>
- </prov:entity>
+ <prov:dictionary prov:id="d2" />
<prov:hadDictionaryMember>
<prov:dictionary prov:ref="d1"/>
@@ -2551,7 +2608,7 @@
<xs:sequence>
<xs:element name="newDictionary" type="prov:IDRef"/>
<xs:element name="oldDictionary" type="prov:IDRef"/>
- <xs:element name="key" type="xs:anySimpleType" maxOccurs="unbounded" />
+ <xs:element name="key" type="xs:anySimpleType" minOccurs=1 maxOccurs="unbounded" />
<xs:element ref="prov:label" minOccurs="0" maxOccurs="unbounded"/>
<xs:element ref="prov:type" minOccurs="0" maxOccurs="unbounded"/>
<xs:any namespace="##other" processContents="lax" minOccurs="0" maxOccurs="unbounded"/>
@@ -2572,13 +2629,9 @@
<prov:entity prov:id="e1"/>
<prov:entity prov:id="e2"/>
- <prov:entity prov:id="d1">
- <prov:type xsi:type="xsd:QName">prov:Dictionary</prov:type>
- </prov:entity>
+ <prov:dictionary prov:id="d1" />
- <prov:entity prov:id="d2">
- <prov:type xsi:type="xsd:QName">prov:Dictionary</prov:type>
- </prov:entity>
+ <prov:dictionary prov:id="d2" />
<prov:hadDictionaryMember>
<prov:dictionary prov:ref="d1"/>
@@ -2649,23 +2702,20 @@
<span class='conditional'>THEN</span> <span class="name">e1 = e2</span>
</p></div>
-<p id="membership-insertion-membership-inference_text">If a dictionary was derived from another dictionary by an insertion, then the former holds all key-entity pairs of the latter, except those updated by the insertion.</p>
+<p id="membership-insertion-membership-inference_text">If a dictionary was derived from another dictionary by an insertion, then the former holds all key-entity pairs of the latter, except those updated by the insertion.
+ Similarly, all members of a dictionary that was derived from another dictionary by an insertion were also members of the latter dictionary, except those added or updated by the insertion.</p>
<div class='inference' id='membership-insertion-membership-inference'>
<span class='ruleTitle'><a class="internalDFN" href="#membership-insertion-membership-inference">Inference D4 (membership-insertion-membership)</a></span>
<p>Here, KV1 is a set of key-entity pairs and K1 is the key-set of KV1.</p>
- <p>
-<span class="conditional">IF</span> <span class="name">prov:hadDictionaryMember(d1, e, k)</span>
+ <ol>
+<li><span class="conditional">IF</span> <span class="name">prov:hadDictionaryMember(d1, e, k)</span>
and <span class="name">prov:derivedByInsertionFrom(d2, d1, KV1)</span> and <span class="name">k</span> ∉ <span class="name">K1</span>
- <span class='conditional'>THEN</span> <span class="name">prov:hadDictionaryMember(d2, e, k)</span>
-</p></div>
-<!--REMOVED CONSTRAINT <p id="membership-update-membership-inference_text">Insertion provides an "update semantics" for the keys that are already present in a dictionary. A new pair replaces an existing pair with the same key in the new dictionary. </p>
- <div class='inference' id='membership-update-membership-inference'>
-<p>
-<span class="conditional">IF</span> <span class="name">hadDictionaryMember(d1, e1, "k1")</span>
- and <span class="name">derivedByInsertionFrom(d2, d1, {("k1", e2)})</span>
- <span class='conditional'>THEN</span> <span class="name">hadDictionaryMember(d2, e2, "k1"))</span>
-</p></div>
-/REMOVED CONSTRAINT-->
+ <span class='conditional'>THEN</span> <span class="name">prov:hadDictionaryMember(d2, e, k)</span></li>
+
+<li><span class="conditional">IF</span> <span class="name">prov:hadDictionaryMember(d2, e, k)</span>
+ and <span class="name">prov:derivedByInsertionFrom(d2, d1, KV1)</span> and <span class="name">k</span> ∉ <span class="name">K1</span>
+ <span class='conditional'>THEN</span> <span class="name">prov:hadDictionaryMember(d1, e, k)</span></li>
+ </ol></div>
<p id="insertion-membership-inference_text">A dictionary that was derived by an insertion of key-entity pairs, holds all these specified key-entity pairs. This inference also means that Insertion provides an "update semantics" for the keys that are already present in a dictionary.</p>
<div class='inference' id='insertion-membership-inference'>
@@ -2673,29 +2723,20 @@
<p>Here, KV1 is a set of key-entity pairs.</p>
<p>
<span class="conditional">IF</span> <span class="name">prov:derivedByInsertionFrom(d2, d1, KV1)</span>
- <span class='conditional'>THEN</span> <span class="name">prov:hadDictionaryMember(d2, e, k) for each (e, k) ∈ KV1</span>
+ <span class='conditional'>THEN</span> <span class="name">prov:hadDictionaryMember(d2, e, k) for each (k, e) ∈ KV1</span>
</p></div>
-
-<!--REMOVED CONSTRAINT <p id="removal-membership-inference_text">Only keys that actually mapped to an entity in a dictionary can be removed from it.</p>
- <div class='inference' id='removal-membership-inference'>
-<p>
-<span class="conditional">IF</span> <span class="name">derivedByRemovalFrom(d2, d1, {"k1"})</span>
- <span class='conditional'>THEN</span> <span class="name">hadDictionaryMember(d1, e1, "k1")</span>
-</p></div>
- <div class="remark"><b>Note from the editors:</b> this constraint seems too restrictive for some implementations, and the editors would like to remove it, unless there is strong consensus to keep it. Removal of this constraint would also allow for duplicate dictionaries to be derived by "removal" of a non-existing key.</div>
-/REMOVED CONSTRAINT-->
-
<p id="insertion-derivation-inference_text">Insertion and removal are special cases of derivation.</p>
<div class='inference' id='insertion-derivation-inference'>
<span class='ruleTitle'><a class="internalDFN" href="#insertion-derivation-inference">Inference D6 (insertion-derivation)</a></span>
- <p>Here, KV1 is a set of key-entity pairs and K1 is a set of keys.</p>
+ <p>Here, KV1 is a set of key-entity pairs.</p>
<p>
<span class="conditional">IF</span> <span class="name">prov:derivedByInsertionFrom(d2, d1, KV1)</span>
<span class='conditional'>THEN</span> <span class="name">prov:wasDerivedFrom(d2, d1)</span>
</p></div>
<div class='inference' id='removal-derivation-inference'>
<span class='ruleTitle'><a class="internalDFN" href="#removal-derivation-inference">Inference D7 (removal-derivation)</a></span>
+ <p>Here, K1 is a set of keys.</p>
<p>
<span class="conditional">IF</span> <span class="name">prov:derivedByRemovalFrom(d2, d1, K1)</span>
<span class='conditional'>THEN</span> <span class="name">prov:wasDerivedFrom(d2, d1)</span>
@@ -2719,7 +2760,7 @@
</ol>
</div>
<div class="remark">
- Note that this inference, together with constraints <a class="internalDFN" href="#impossible-removal-insertion-constraint">D9</a>, <a class="internalDFN" href="#impossible-insertion-insertion-constraint">D10</a> and <a class="internalDFN" href="#impossible-removal-removal-constraint">D11</a>, and the fact that an EmptyDictionary does not contain any key-entity pairs, guarantees <b>completeness</b> of a dictionary, if it can be traced back to an EmptyDictionary through insertions and removals.
+ Note that this inference, together with constraints <a class="internalDFN" href="#impossible-removal-insertion-constraint">D9</a>, <a class="internalDFN" href="#unique-insertion-constraint">D10</a> and <a class="internalDFN" href="#unique-removal-constraint">D11</a>, and the fact that an EmptyDictionary does not contain any key-entity pairs, guarantees <b>completeness</b> of a dictionary, if it can be traced back to an EmptyDictionary through insertions and removals.
Here, completeness means that all key-entity pairs of the dictionary are known through a hadDictionaryMember statement.
</div>
@@ -2742,26 +2783,28 @@
<p id="impossible-removal-insertion_text">A dictionary must not be derived through multiple insertion or removal relations.</p>
<div class='constraint' id='impossible-removal-insertion-constraint'>
<span class='ruleTitle'><a class="internalDFN" href="#impossible-removal-insertion-constraint">Constraint D10 (impossible-removal-insertion)</a></span>
- <p>Here, <span class="name">K1</span> is a set of keys and <span class="name">KV2</span> is a set of key-entity pairs.</p>
+ <p>Here, <span class="name">K0</span> is a set of keys and <span class="name">KV1</span> is a set of key-entity pairs.</p>
<p>
-<span class="conditional">IF</span> <span class="name">prov:derivedByRemovalFrom(d2, d1, K1)</span> and
- <span class="name">prov:derivedByInsertionFrom(d2, d1, KV2)</span><span class='conditional'>THEN</span> <span
+<span class="conditional">IF</span> <span class="name">prov:derivedByRemovalFrom(d2, d0, K0)</span> and
+ <span class="name">prov:derivedByInsertionFrom(d2, d1, KV1)</span><span class='conditional'>THEN</span> <span
class="conditional">INVALID</span>
</p></div>
-<div class='constraint' id='impossible-insertion-insertion-constraint'>
- <span class='ruleTitle'><a class="internalDFN" href="#impossible-insertion-insertion-constraint">Constraint D10 (impossible-insertion-insertion)</a></span>
-<p>Here, <span class="name">KV1</span> and <span class="name">KV2</span> are sets of key-entity pairs.</p>
+<div class='constraint' id='unique-insertion-constraint'>
+ <span class='ruleTitle'><a class="internalDFN" href="#unique-insertion-constraint">Constraint D11 (unique-insertion)</a></span>
+<p>Here, <span class="name">KV0</span> and <span class="name">KV1</span> are sets of key-entity pairs.</p>
<p>
-<span class="conditional">IF</span> <span class="name">prov:derivedByInsertionFrom(d2, d1, KV1)</span> and
- <span class="name">prov:derivedByInsertionFrom(d2, d1, KV2)</span><span class='conditional'>THEN</span> <span
+<span class="conditional">IF</span> <span class="name">prov:derivedByInsertionFrom(d2, d0, KV0)</span> and
+ <span class="name">prov:derivedByInsertionFrom(d2, d1, KV1)</span><span class='conditional'>THEN</span> <span
+ class="name">d0 = d1</span> and <span
class="name">KV1 = KV2</span>
</p></div>
-<div class='constraint' id='impossible-removal-removal-constraint'>
- <span class='ruleTitle'><a class="internalDFN" href="#impossible-removal-removal-constraint">Constraint D12 (impossible-removal-removal)</a></span>
-<p>Here, <span class="name">K1</span> and <span class="name">K2</span> are sets of keys.</p>
+<div class='constraint' id='unique-removal-constraint'>
+ <span class='ruleTitle'><a class="internalDFN" href="#unique-removal-constraint">Constraint D12 (unique-removal)</a></span>
+<p>Here, <span class="name">K0</span> and <span class="name">K1</span> are sets of keys.</p>
<p>
-<span class="conditional">IF</span> <span class="name">prov:derivedByRemovalFrom(d2, d1, K1)</span> and
- <span class="name">prov:derivedByRemovalFrom(d2, d1, K2)</span><span class='conditional'>THEN</span> <span
+<span class="conditional">IF</span> <span class="name">prov:derivedByRemovalFrom(d2, d0, K0)</span> and
+ <span class="name">prov:derivedByRemovalFrom(d2, d1, K1)</span><span class='conditional'>THEN</span> <span
+ class="name">d0 = d1</span> and <span
class="name">K1 = K2</span>
</p></div>
@@ -2824,10 +2867,30 @@
</section>
+<section class="appendix">
+<h2>Change Log</h2>
+<section>
+ <h3>Change Log Since First Public Working Draft</h3>
+<ul>
+<li>Added the full title of the document.</li>
+<li>Added namespace and convention sections.</li>
+<li>Made <span class="name">prov:</span> prefix explicit.</li>
+<li>Changed all mentions of "key-value pair" to the more accurate "key-entity pair".</li>
+<li>Clarified that insertions and removals are to be seen as differences rather than as operations in the context of provenance.</li>
+<li>Updated PROV-N grammar.</li>
+<li>Made <a href="#qualifiedInsertion">prov:qualifiedInsertion</a> and <a href="#qualifiedRemoval">prov:qualifiedRemoval</a> sub-properties of <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/#qualifiedDerivation">qualifiedDerivation</a>.</li>
+<li>Updated XML schema definition.</li>
+<li>Added an notations and conventions paragraph to the constraints.</li>
+<li>Added <a href="#cmembership-dmembership-inference">inference D2</a> (collection-membership-dictionary-membership).</li>
+<li>Various corrections</li>
+</ul>
+</section>
+</section>
<section class="appendix">
<h2>Acknowledgements</h2>
+ <p>This document has been produced by the PROV Working Group, and its contents reflect extensive discussion within the Working Group as a whole.</p>
<p>
Members of the Provenance Working Group at the time of publication of this document were: Ilkay Altintas (Invited expert), Reza B'Far (Oracle Corporation), Khalid Belhajjame (University of Manchester), James Cheney (University of Edinburgh, School of Informatics), Sam Coppens (iMinds - Ghent University), David Corsar (University of Aberdeen, Computing Science), Stephen Cresswell (The National Archives), Tom De Nies (iMinds - Ghent University), Helena Deus (DERI Galway at the National University of Ireland, Galway, Ireland), Simon Dobson (Invited expert), Martin Doerr (Foundation for Research and Technology - Hellas(FORTH)), Kai Eckert (Invited expert), Jean-Pierre EVAIN (European Broadcasting Union, EBU-UER), James Frew (Invited expert), Irini Fundulaki (Foundation for Research and Technology - Hellas(FORTH)), Daniel Garijo (Universidad Politécnica de Madrid), Yolanda Gil (Invited expert), Ryan Golden (Oracle Corporation), Paul Groth (Vrije Universiteit), Olaf Hartig (Invited expert), David Hau (National Cancer Institute, NCI), Sandro Hawke (W3C/MIT), Jörn Hees (German Research Center for Artificial Intelligence (DFKI) Gmbh), Ivan Herman, (W3C/ERCIM), Ralph Hodgson (TopQuadrant), Hook Hua (Invited expert), Trung Dong Huynh (University of Southampton), Graham Klyne (University of Oxford), Michael Lang (Revelytix, Inc.), Timothy Lebo (Rensselaer Polytechnic Institute), James McCusker (Rensselaer Polytechnic Institute), Deborah McGuinness (Rensselaer Polytechnic Institute), Simon Miles (Invited expert), Paolo Missier (School of Computing Science, Newcastle university), Luc Moreau (University of Southampton), James Myers (Rensselaer Polytechnic Institute), Vinh Nguyen (Wright State University), Edoardo Pignotti (University of Aberdeen, Computing Science), Paulo da Silva Pinheiro (Rensselaer Polytechnic Institute), Carl Reed (Open Geospatial Consortium), Adam Retter (Invited Expert), Christine Runnegar (Invited expert), Satya Sahoo (Invited expert), David Schaengold (Revelytix, Inc.), Daniel Schutzer (FSTC, Financial Services Technology Consortium), Yogesh Simmhan (Invited expert), Stian Soiland-Reyes (University of Manchester), Eric Stephan (Pacific Northwest National Laboratory), Linda Stewart (The National Archives), Ed Summers (Library of Congress), Maria Theodoridou (Foundation for Research and Technology - Hellas(FORTH)), Ted Thibodeau (OpenLink Software Inc.), Curt Tilmes (National Aeronautics and Space Administration), Craig Trim (IBM Corporation), Stephan Zednik (Rensselaer Polytechnic Institute), Jun Zhao (University of Oxford), Yuting Zhao (University of Aberdeen, Computing Science).
</p>
--- a/dictionary/prov-dictionary-grammar.txt Sun Apr 14 19:43:18 2013 +0200
+++ b/dictionary/prov-dictionary-grammar.txt Sun Apr 14 19:44:18 2013 +0200
@@ -1,4 +1,4 @@
-[1] membershipExpression ::= "hadDictionaryMember" "(" dIdentifier "," eIdentifier "," key ")"
+[1] dictionaryMembershipExpression ::= "hadDictionaryMember" "(" dIdentifier "," eIdentifier "," key ")"
[2] derivationByInsertionFromExpression ::= "derivedByInsertionFrom" "(" optionalIdentifier ";" dIdentifier "," dIdentifier "," "{" keyEntityPairs "}" "," optionalAttributeValuePairs ")"
[3] derivationByRemovalFromExpression ::= "derivedByRemovalFrom" "(" optionalIdentifier ";" dIdentifier "," dIdentifier "," "{" keySet "}" "," optionalAttributeValuePairs ")"
[4] dIdentifier ::= identifier
--- a/dictionary/prov-dictionary.owl Sun Apr 14 19:43:18 2013 +0200
+++ b/dictionary/prov-dictionary.owl Sun Apr 14 19:44:18 2013 +0200
@@ -46,7 +46,7 @@
<constraints rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#dictionary-constraints</constraints>
<n rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#expression-dictionary-insertion</n>
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-insertion</dm>
- <definition>The dictionary was derived from the other by insertion. prov:qualifiedInsertion shows details of the insertion, in particular the inserted key-entity pairs.</definition>
+ <definition>The dictionary was derived from the other by insertion. Can be qualified with prov:qualifiedInsertion, which shows details of the insertion, in particular the inserted key-entity pairs.</definition>
<component>collections</component>
<category>collections</category>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
@@ -65,7 +65,7 @@
<n rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#expression-dictionary-removal</n>
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-removal</dm>
<component>collections</component>
- <definition>The dictionary was derived from the other by removal. prov:qualifiedRemoval shows details of the removal, in particular the removed key-entity pairs.</definition>
+ <definition>The dictionary was derived from the other by removal. Can be qualified with prov:qualifiedRemoval, which shows details of the removal, in particular the removed keys.</definition>
<category>collections</category>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
<rdfs:range rdf:resource="http://www.w3.org/ns/prov#Dictionary"/>
@@ -139,7 +139,7 @@
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-membership</dm>
<category>collections</category>
<component>collections</component>
- <definition>The value of a KeyEntityPair.</definition>
+ <definition>The entity of a prov:KeyEntityPair, which is an element of a prov:Dictionary.</definition>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
<rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
<rdfs:domain rdf:resource="http://www.w3.org/ns/prov#KeyEntityPair"/>
@@ -154,7 +154,7 @@
<constraints rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#dictionary-constraints</constraints>
<n rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#expression-dictionary-insertion</n>
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-insertion</dm>
- <definition>The dictionary was derived from the other by insertion. prov:qualifiedInsertion shows details of the insertion, in particular the inserted key-entity pairs.</definition>
+ <definition>prov:qualifiedInsertion shows the details of an insertion, in particular the inserted key-entity pairs.</definition>
<category>collections</category>
<component>collections</component>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
@@ -174,7 +174,7 @@
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-removal</dm>
<category>collections</category>
<component>collections</component>
- <definition>The dictionary was derived from the other by removal. prov:qualifiedRemoval shows details of the removal, in particular the removed keys.</definition>
+ <definition>prov:qualifiedRemoval shows the details of a removal, in particular the removed keys.</definition>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
<rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Dictionary"/>
<rdfs:range rdf:resource="http://www.w3.org/ns/prov#Removal"/>
@@ -202,7 +202,7 @@
<n rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#expression-dictionary-membership</n>
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-membership</dm>
<component>collections</component>
- <definition>The key of a KeyEntityPair, which is an element of a prov:Dictionary.</definition>
+ <definition>The key of a prov:KeyEntityPair, which is an element of a prov:Dictionary.</definition>
<category>collections</category>
<rdfs:range rdf:resource="&rdfs;Literal"/>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
@@ -291,7 +291,7 @@
<constraints rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#dictionary-constraints</constraints>
<n rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#expression-dictionary-insertion</n>
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-insertion</dm>
- <definition>Insertion is a derivation that transforms a dictionary into another, by insertion of one or more key-entity pairs.</definition>
+ <definition>Insertion is a derivation that describes the transformation of a dictionary into another, by insertion of one or more key-entity pairs.</definition>
<category>collections</category>
<component>collections</component>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
@@ -348,7 +348,7 @@
<n rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#expression-dictionary-removal</n>
<dm rdf:datatype="&xsd;anyURI">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/#term-dictionary-removal</dm>
<category>collections</category>
- <definition>Removal is a derivation that transforms a dictionary into another, by removing one or more key-entity pairs.</definition>
+ <definition>Removal is a derivation that describes the transformation of a dictionary into another, by removing one or more keys.</definition>
<component>collections</component>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
<unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#derivedByRemovalFrom"/>
--- a/links/diff.html Sun Apr 14 19:43:18 2013 +0200
+++ b/links/diff.html Sun Apr 14 19:44:18 2013 +0200
@@ -17,7 +17,7 @@
color: #b9ab2d;
}
div.issue-title { color: #e05252; }
-div.note-title { color: #52e052; }
+div.note-title { color: <span class="delete">#52e052;</span><span class="insert">#2b2;</span> }
div.issue-title span, div.note-title span {
text-transform: uppercase;
}
@@ -32,7 +32,7 @@
border-left-style: solid;
}
div.issue, div.note {
- padding: 0.5em;
+ padding:<span class="insert"> 1em 1.2em</span> 0.5em;
margin: 1em 0;
position: relative;
clear: both;
@@ -855,7 +855,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and <span class="delete">Dublic</span><span class="insert">Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles (this document).</li>
</ul>
@@ -955,7 +955,7 @@
<p>This <span class="delete">document</span><span class="insert">specification</span> introduces a new concept <a href="#concept-mention" class="internalDFN">Mention</a> allowing an entity to be described as the specialization of another entity, itself described in another bundle. <span class="delete">The document</span><span class="insert">This specification</span> provides not only a conceptual definition of <a href="#concept-mention" class="internalDFN">Mention</a>, but also the corresponding ontological, schema, and notational definitions, for the various representations of PROV. It also includes constraints that apply to this construct specifically. It is our aim to promote interoperability by defining <a href="#concept-mention" class="internalDFN">Mention</a> conceptually and in the representations of PROV.</p>
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">The concept <a href="#concept-mention" class="internalDFN">Mention</a> is experimental, and for this reason was not defined in PROV recommendation-track documents. The Provenance Working Group is seeking feedback from the community on its usefulness in practical scenarios.
+<div class="note"><div class="note-title" role="heading" aria-level="3"><span>Note</span></div><div class="">The concept <a href="#concept-mention" class="internalDFN">Mention</a> is experimental, and for this reason was not defined in PROV recommendation-track documents. The Provenance Working Group is seeking feedback from the community on its usefulness in practical scenarios.
</div></div>
--- a/links/prov-links.html Sun Apr 14 19:43:18 2013 +0200
+++ b/links/prov-links.html Sun Apr 14 19:44:18 2013 +0200
@@ -750,7 +750,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [[PROV-DC]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [[PROV-DC]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles (this document).</li>
</ul>
--- a/links/releases/NOTE-prov-links-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/links/releases/NOTE-prov-links-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -10,7 +10,7 @@
color: #b9ab2d;
}
div.issue-title { color: #e05252; }
-div.note-title { color: #52e052; }
+div.note-title { color: #2b2; }
div.issue-title span, div.note-title span {
text-transform: uppercase;
}
@@ -25,7 +25,7 @@
border-left-style: solid;
}
div.issue, div.note {
- padding: 0.5em;
+ padding: 1em 1.2em 0.5em;
margin: 1em 0;
position: relative;
clear: both;
@@ -838,7 +838,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles (this document).</li>
</ul>
@@ -931,7 +931,7 @@
<p>This specification introduces a new concept <a href="#concept-mention" class="internalDFN">Mention</a> allowing an entity to be described as the specialization of another entity, itself described in another bundle. This specification provides not only a conceptual definition of <a href="#concept-mention" class="internalDFN">Mention</a>, but also the corresponding ontological, schema, and notational definitions, for the various representations of PROV. It also includes constraints that apply to this construct specifically. It is our aim to promote interoperability by defining <a href="#concept-mention" class="internalDFN">Mention</a> conceptually and in the representations of PROV.</p>
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">The concept <a href="#concept-mention" class="internalDFN">Mention</a> is experimental, and for this reason was not defined in PROV recommendation-track documents. The Provenance Working Group is seeking feedback from the community on its usefulness in practical scenarios.
+<div class="note"><div class="note-title" role="heading" aria-level="3"><span>Note</span></div><div class="">The concept <a href="#concept-mention" class="internalDFN">Mention</a> is experimental, and for this reason was not defined in PROV recommendation-track documents. The Provenance Working Group is seeking feedback from the community on its usefulness in practical scenarios.
</div></div>
--- a/links/releases/NOTE-prov-links-20130430/diff.html Sun Apr 14 19:43:18 2013 +0200
+++ b/links/releases/NOTE-prov-links-20130430/diff.html Sun Apr 14 19:44:18 2013 +0200
@@ -17,7 +17,7 @@
color: #b9ab2d;
}
div.issue-title { color: #e05252; }
-div.note-title { color: #52e052; }
+div.note-title { color: <span class="delete">#52e052;</span><span class="insert">#2b2;</span> }
div.issue-title span, div.note-title span {
text-transform: uppercase;
}
@@ -32,7 +32,7 @@
border-left-style: solid;
}
div.issue, div.note {
- padding: 0.5em;
+ padding:<span class="insert"> 1em 1.2em</span> 0.5em;
margin: 1em 0;
position: relative;
clear: both;
@@ -855,7 +855,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and <span class="delete">Dublic</span><span class="insert">Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles (this document).</li>
</ul>
@@ -955,7 +955,7 @@
<p>This <span class="delete">document</span><span class="insert">specification</span> introduces a new concept <a href="#concept-mention" class="internalDFN">Mention</a> allowing an entity to be described as the specialization of another entity, itself described in another bundle. <span class="delete">The document</span><span class="insert">This specification</span> provides not only a conceptual definition of <a href="#concept-mention" class="internalDFN">Mention</a>, but also the corresponding ontological, schema, and notational definitions, for the various representations of PROV. It also includes constraints that apply to this construct specifically. It is our aim to promote interoperability by defining <a href="#concept-mention" class="internalDFN">Mention</a> conceptually and in the representations of PROV.</p>
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">The concept <a href="#concept-mention" class="internalDFN">Mention</a> is experimental, and for this reason was not defined in PROV recommendation-track documents. The Provenance Working Group is seeking feedback from the community on its usefulness in practical scenarios.
+<div class="note"><div class="note-title" role="heading" aria-level="3"><span>Note</span></div><div class="">The concept <a href="#concept-mention" class="internalDFN">Mention</a> is experimental, and for this reason was not defined in PROV recommendation-track documents. The Provenance Working Group is seeking feedback from the community on its usefulness in practical scenarios.
</div></div>
--- a/model/diff-c.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/diff-c.html Sun Apr 14 19:44:18 2013 +0200
@@ -815,7 +815,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV and Dublic</span><span class="insert">PROV-O and Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
@@ -902,7 +902,7 @@
</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1. </span>Introduction<br>
-</a><ul class="toc"><li class="tocline"><a href="#conventions" class="tocxref"><span class="secno">1.1 </span>Conventions</a></li><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.2 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.3 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.4 </span> Audience </a></li></ul></li><li class="tocline"><a href="#rationale" class="tocxref"><span class="secno">2. </span>Rationale (Informative)</a><ul class="toc"><li class="tocline"><a href="#entities-activities-and-agents" class="tocxref"><span class="secno">2.1 </span>Entities, Activities and Agents</a></li><li class="tocline"><a href="#events" class="tocxref"><span class="secno">2.2 </span>Events</a></li><li class="tocline"><a href="#typing-section" class="tocxref"><span class="secno">2.3 </span>Types</a></li><li class="tocline"><a href="#overview" class="tocxref"><span class="secno">2.4 </span>Validation Process Overview</a></li><li class="tocline"><a href="#summary-of-inferences-and-constraints" class="tocxref"><span class="secno">2.5 </span>Summary of inferences and constraints</a></li></ul></li><li class="tocline"><a href="#compliance" class="tocxref"><span class="secno">3. </span>Compliance with this document</a></li><li class="tocline"><a href="#concepts" class="tocxref"><span class="secno">4. </span>Basic concepts</a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5. </span>Definitions and Inferences</a><ul class="toc"><li class="tocline"><a href="#optional-identifiers-and-attributes" class="tocxref"><span class="secno">5.1 </span>Optional Identifiers and Attributes</a></li><li class="tocline"><a href="#entities-and-activities" class="tocxref"><span class="secno">5.2 </span>Entities and Activities</a></li><li class="tocline"><a href="#derivations" class="tocxref"><span class="secno">5.3 </span>Derivations</a></li><li class="tocline"><a href="#agents" class="tocxref"><span class="secno">5.4 </span>Agents</a></li><li class="tocline"><a href="#alternate-and-specialized-entities" class="tocxref"><span class="secno">5.5 </span>Alternate and Specialized Entities</a></li></ul></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">6. </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">6.1 </span>Uniqueness Constraints</a></li><li class="tocline"><a href="#event-ordering-constraints" class="tocxref"><span class="secno">6.2 </span>Event Ordering Constraints</a><ul class="toc"><li class="tocline"><a href="#activity-constraints" class="tocxref"><span class="secno">6.2.1 </span>Activity constraints</a></li><li class="tocline"><a href="#entity-constraints" class="tocxref"><span class="secno">6.2.2 </span> Entity constraints</a></li><li class="tocline"><a href="#agent-constraints" class="tocxref"><span class="secno">6.2.3 </span> Agent constraints</a></li></ul></li><li class="tocline"><a href="#type-constraints" class="tocxref"><span class="secno">6.3 </span>Type Constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">6.4 </span>Impossibility constraints</a></li></ul></li><li class="tocline"><a href="#normalization-validity-equivalence" class="tocxref"><span class="secno">7. </span>Normalization, Validity, and Equivalence</a><ul class="toc"><li class="tocline"><a href="#instances" class="tocxref"><span class="secno">7.1 </span>Instances</a></li><li class="tocline"><a href="#bundle-constraints" class="tocxref"><span class="secno">7.2 </span>Bundles and Documents</a></li></ul></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno">8. </span>Glossary</a></li><li class="tocline"><a href="#termination" class="tocxref"><span class="secno">A. </span>Termination of normalization</a></li><li class="tocline"><a href="#change-log" class="tocxref"><span class="secno">B. </span>Change Log</a><ul class="toc"><li class="tocline"><a href="#changes-since-proposed-recommendation" class="tocxref"><span class="secno"><span class="insert">B.1 </span></span><span class="insert">Changes since Proposed Recommendation</span></a></li><li class="tocline"><a href="#changes-from-candidate-recommendation-to-this-version" class="tocxref"><span class="secno"><span class="delete">B.1</span><span class="insert">B.2</span> </span>Changes from Candidate Recommendation to this version</a></li><li class="tocline"><a href="#changes-from-last-call-working-draft-to-candidate-recommendation" class="tocxref"><span class="secno"><span class="delete">B.2</span><span class="insert">B.3</span> </span>Changes from Last Call Working Draft to Candidate Recommendation</a></li></ul></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">C. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">D. </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">D.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">D.2 </span>Informative references</a></li></ul></li></ul></section>
+</a><ul class="toc"><li class="tocline"><a href="#conventions" class="tocxref"><span class="secno">1.1 </span>Conventions</a></li><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.2 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.3 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.4 </span> Audience </a></li></ul></li><li class="tocline"><a href="#rationale" class="tocxref"><span class="secno">2. </span>Rationale (Informative)</a><ul class="toc"><li class="tocline"><a href="#entities-activities-and-agents" class="tocxref"><span class="secno">2.1 </span>Entities, Activities and Agents</a></li><li class="tocline"><a href="#events" class="tocxref"><span class="secno">2.2 </span>Events</a></li><li class="tocline"><a href="#typing-section" class="tocxref"><span class="secno">2.3 </span>Types</a></li><li class="tocline"><a href="#overview" class="tocxref"><span class="secno">2.4 </span>Validation Process Overview</a></li><li class="tocline"><a href="#summary-of-inferences-and-constraints" class="tocxref"><span class="secno">2.5 </span>Summary of inferences and constraints</a></li></ul></li><li class="tocline"><a href="#compliance" class="tocxref"><span class="secno">3. </span>Compliance with this document</a></li><li class="tocline"><a href="#concepts" class="tocxref"><span class="secno">4. </span>Basic concepts</a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5. </span>Definitions and Inferences</a><ul class="toc"><li class="tocline"><a href="#optional-identifiers-and-attributes" class="tocxref"><span class="secno">5.1 </span>Optional Identifiers and Attributes</a></li><li class="tocline"><a href="#entities-and-activities" class="tocxref"><span class="secno">5.2 </span>Entities and Activities</a></li><li class="tocline"><a href="#derivations" class="tocxref"><span class="secno">5.3 </span>Derivations</a></li><li class="tocline"><a href="#agents" class="tocxref"><span class="secno">5.4 </span>Agents</a></li><li class="tocline"><a href="#alternate-and-specialized-entities" class="tocxref"><span class="secno">5.5 </span>Alternate and Specialized Entities</a></li></ul></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">6. </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">6.1 </span>Uniqueness Constraints</a></li><li class="tocline"><a href="#event-ordering-constraints" class="tocxref"><span class="secno">6.2 </span>Event Ordering Constraints</a><ul class="toc"><li class="tocline"><a href="#activity-constraints" class="tocxref"><span class="secno">6.2.1 </span>Activity constraints</a></li><li class="tocline"><a href="#entity-constraints" class="tocxref"><span class="secno">6.2.2 </span> Entity constraints</a></li><li class="tocline"><a href="#agent-constraints" class="tocxref"><span class="secno">6.2.3 </span> Agent constraints</a></li></ul></li><li class="tocline"><a href="#type-constraints" class="tocxref"><span class="secno">6.3 </span>Type Constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">6.4 </span>Impossibility constraints</a></li></ul></li><li class="tocline"><a href="#normalization-validity-equivalence" class="tocxref"><span class="secno">7. </span>Normalization, Validity, and Equivalence</a><ul class="toc"><li class="tocline"><a href="#instances" class="tocxref"><span class="secno">7.1 </span>Instances</a></li><li class="tocline"><a href="#bundle-constraints" class="tocxref"><span class="secno">7.2 </span>Bundles and Documents</a></li></ul></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno">8. </span>Glossary</a></li><li class="tocline"><a href="#termination" class="tocxref"><span class="secno">A. </span>Termination of normalization</a></li><li class="tocline"><a href="#change-log" class="tocxref"><span class="secno">B. </span>Change Log</a><ul class="toc"><li class="tocline"><a href="#changes-since-proposed-recommendation" class="tocxref"><span class="secno">B.1 </span>Changes <span class="insert">since Proposed Recommendation</span></a></li><li class="tocline"><a href="#changes-from-candidate-recommendation-to-proposed-recommendation" class="tocxref"><span class="secno"><span class="insert">B.2 </span></span><span class="insert">Changes </span>from Candidate Recommendation to <span class="delete">this version</span><span class="insert">Proposed Recommendation</span></a></li><li class="tocline"><a href="#changes-from-last-call-working-draft-to-candidate-recommendation" class="tocxref"><span class="secno"><span class="delete">B.2</span><span class="insert">B.3</span> </span>Changes from Last Call Working Draft to Candidate Recommendation</a></li></ul></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">C. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">D. </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">D.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">D.2 </span>Informative references</a></li></ul></li></ul></section>
@@ -1434,8 +1434,8 @@
implementers, while the procedural approach adopted here immediately demonstrates
implementability and provides an adequate (polynomial-time) default implementation. In
this section we relate the declarative meaning of formulas to their
-procedural meaning. [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>] will provide an alternative,
-declarative characterization of validity and equivalence which could
+procedural meaning. [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>] <span class="delete">will provide</span><span class="insert">provides</span> an alternative,
+declarative characterization of validity<span class="delete"> and equivalence</span> which could
be used as a starting point for other implementation strategies. </p>
@@ -1477,7 +1477,7 @@
</p>
- <h4 id="substitution-1">Substitution</h4><p><em>This section is non-normative.</em></p>
+ <h3 id="substitution-1">Substitution<span class="delete">This section is non-normative.</span></h3>
<p>A <em>substitution</em> is a function that maps variables to terms. Concretely, since we only
need to consider substitutions of finite sets of variables, we can
write substitutions as <span class="math">[x<sub>1</sub> = t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span>. A substitution
@@ -1499,7 +1499,7 @@
- <h4 id="formulas">Formulas</h4>
+ <h3 id="formulas">Formulas</h3>
<p>
For the purpose of constraint checking, we view PROV statements
(possibly involving existential variables) as
@@ -1514,7 +1514,7 @@
<li>Uniqueness constraints employ atomic equational formulas <span class="math">t =
t'</span>.</li>
<li>Ordering constraints employ atomic precedence relations that can
- be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math">strictly_precedes(t,t')</span>
+ be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math"><span class="delete">strictly_precedes(t,t')</span><span class="insert">strictlyPrecedes(t,t')</span></span>
</li>
<li>Typing constraints <span class="name">'type' ∈ typeOf(id)</span>
can be represented as a atomic formulas <span class="name">typeOf(id,'type')</span>.
@@ -1529,24 +1529,24 @@
background on logical formulas, see a logic textbook such as [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>].</p>
<ul>
<li>
- A definition of the form <span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>
+ A definition of the form <span class="insert">"</span><span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span><span class="insert">"</span>
can be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A ⇔ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the definition.
</li>
-<li>An inference of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span> can
+<li>An inference of the form <span class="insert">"</span><span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span><span class="insert">"</span> can
be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the inference.
</li>
-<li>A uniqueness, ordering, or typing constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span> can be viewed as a formula
+<li>A uniqueness, ordering, or typing constraint of the form <span class="insert">"</span><span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span><span class="insert">"</span> can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ C</span>. </li>
-<li>A constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span> can be viewed as a formula
+<li>A constraint of the form <span class="insert">"</span><span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span><span class="insert">"</span> can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ False</span>. </li>
</ul>
- <h4 id="satisfying-definitions-inferences-and-constraints">Satisfying definitions, inferences, and constraints</h4>
+ <h3 id="satisfying-definitions-inferences-and-constraints">Satisfying definitions, inferences, and constraints</h3>
<p>
In logic, a formula's meaning is defined by saying when it is
<em>satisfied</em>. We can view
@@ -1565,7 +1565,7 @@
B<sub>k</sub></span> are either both true or both false.
</li>
<li>A logical implication as used in an inference is
- satisfied with the formula <span class="math">∀
+ satisfied <span class="delete">with</span><span class="insert">when</span> the formula <span class="math">∀
x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> holds, that is, for any substitution of
@@ -1586,7 +1586,7 @@
substitution for <span class="math">x<sub>1</sub>...x<sub>n</sub></span> making <span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> true.
</li></ol>
-<h4 id="unification-and-merging">Unification and Merging</h4>
+<h3 id="unification-and-merging">Unification and Merging</h3>
<p><em>Unification</em> is an operation that takes two terms and compares them to
determine whether they can be made equal by substituting an
@@ -1609,7 +1609,7 @@
- <h4 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h4>
+ <h3 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h3>
<p>Formulas can also be interpreted as having computational
content. That is, if an instance does not satisfy a formula, we can
often <em>apply</em> the formula to the instance to produce another
@@ -1635,7 +1635,7 @@
x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> can be applied by searching for any occurrences of <span class="math"> A<sub>1</sub> ∧ ... ∧
- A<sub>p</sub></span> in the instance and, for each such match,
+ A<sub>p</sub></span> in the instance and, for each such <span class="delete">match,</span><span class="insert">match</span>
for which the entire conclusion does not already hold (for some <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>),
adding <span class="math">B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> to the instance, generating fresh existential
@@ -1682,7 +1682,7 @@
</p>
- <h4 id="termination-1">Termination</h4>
+ <h3 id="termination-1">Termination</h3>
<p>
In general, applying sets of logical formulas of the above
definition, inference, and constraint forms is not guaranteed to
@@ -1745,7 +1745,7 @@
</div>
- <h4 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h4>
+ <h3 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h3>
<p>
The ordering, typing, and impossibility constraints are checked
rather than applied. This means that they do not generate new
@@ -1811,7 +1811,7 @@
- <h4 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h4>
+ <h3 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h3>
<p> Given two normal forms, a natural question is whether they contain
the same information, that is, whether they are equivalent (if so,
then the original instances are also equivalent.) By analogy with
@@ -1865,7 +1865,7 @@
<li>every pair of invalid instances are equivalent</li>
</ol>
-<h4 id="from-instances-to-bundles-and-documents">From Instances to Bundles and Documents</h4>
+<h3 id="from-instances-to-bundles-and-documents">From Instances to Bundles and Documents</h3>
<p>PROV documents can contain multiple instances: a <a href="#dfn-toplevel-instance" class="internalDFN">toplevel
instance</a>, and
@@ -2501,7 +2501,8 @@
<div class="remark">
- <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a> and <a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a>.
+ <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a> and <a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a><span class="delete">.
+</span>
do not apply to <span class="name">alternateOf</span> and <span class="name">specializationOf</span>, which do not have identifiers and attributes.
</p>
</div>
@@ -2643,7 +2644,7 @@
Essentially, the definitions state that parameters
<span class="name">g,u</span> are expandable only if the activity is specified, i.e., if parameter <span class="name">a</span> is provided.
-The rationale for this is that when a is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
+The rationale for this is that when <span class="name">a</span> is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
<p> A later constraint, <a class="rule-ref" href="#impossible-unspecified-derivation-generation-use"><span>Constraint 51 (impossible-unspecified-derivation-generation-use)</span></a>,
@@ -4145,7 +4146,7 @@
That is, <span class="name">typeOf(e)</span> returns the set of types
associated with identifier <span class="name">e</span>. The function
<span class="name">typeOf</span> is not a PROV statement, but a
-construct used only during validation PROV, similar to <a href="#dfn-precedes" class="internalDFN">precedes</a>.
+construct used only during <span class="delete">validation PROV,</span><span class="insert">validation,</span> similar to <a href="#dfn-precedes" class="internalDFN">precedes</a>.
</p>
@@ -4521,10 +4522,23 @@
<a title="equivalence">equivalence</a> of PROV documents and instances. We first define these concepts
for PROV instances and then extend them to PROV documents.</p>
-<section id="instances">
+<div class="remark"><span class="insert">
+ Implementations should expand
+ namespace prefixes and perform any appropriate reasoning about
+ co-reference of identifiers, and rewrite the instance (by
+ replacing co-referent identifiers with a single common identifier) to
+ make this explicit, before doing validation, equivalence checking,
+ or normalization.
+ All of the following definitions assume that the application has
+ already determined which URIs in the PROV instance are co-referent
+ (e.g. </span><span class="name"><span class="insert">owl:sameAs</span></span><span class="insert"> as a result of OWL
+ reasoning).
+ </span></div>
+
+ <section id="instances">
<h3><span class="secno">7.1 </span>Instances</h3>
-<div class="remark">
+<span class="delete">
Before normalization or validation, implementations should expand
namespace prefixes and perform any appropriate reasoning about
co-reference of identifiers, and rewrite the instance (by
@@ -4533,9 +4547,12 @@
or normalization.
All of the following definitions assume that the application has
already determined which URIs in the PROV instance are co-referent
- (e.g. <span class="name">owl:sameAs</span> as a result of OWL
+ (e.g. </span><span class="delete">owl:sameAs</span><span class="delete"> as a result of OWL
reasoning).
- </div>
+ </span>
+
+
+
<p> We define the <dfn id="dfn-normal-form">normal form</dfn> of a PROV instance as the set
of provenance statements resulting from applying all definitions,
@@ -4794,8 +4811,9 @@
attributes would also arise from one with no attributes.
</p>
- <p><b>Termination for instances without attributes.</b> For
+ <p><b>Termination for instances without attributes.</b><span class="delete"> For
these instances, uniqueness and key constraints can be
+ </span>
As shown in [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>], termination of normalization can be
shown by checking that the inference rules are <em>weakly
acyclic</em>. In addition, weak acyclicity can be checked
@@ -4923,13 +4941,20 @@
<ul>
<li><span class="insert"> Changed the status of this document section.
</span></li><li><span class="insert"> Changed all URLs to PROV documents.
+ </span></li><li><span class="insert"> Fixed some minor typos in section 2.4.
+ </span></li><li><span class="insert"> Fixed typo in remark after definition 2.
+ </span></li><li><span class="insert"> Fixed typo in paragraph after table 2.
+ </span></li><li><span class="insert"> Fixed typo in sec. 6.3.
+ </span></li><li><span class="insert"> Fixed wording in remark in sec. 7.1, and moved it before
+ section heading.
+ </span></li><li><span class="insert"> Fixed typo in appendix A.
</span></li></ul>
</section>
-<section class="appendix" id="changes-from-candidate-recommendation-to-this-version">
- <h3><span class="secno"><span class="delete">B.1</span><span class="insert">B.2</span> </span>Changes from Candidate Recommendation to this version</h3>
+<section class="appendix" id="changes-from-candidate-recommendation-to-proposed-recommendation">
+ <h3><span class="secno"><span class="delete">B.1</span><span class="insert">B.2</span> </span>Changes from Candidate Recommendation to <span class="delete">this version</span><span class="insert">Proposed Recommendation</span></h3>
<p> Please see the <a href="http://www.w3.org/2011/prov/wiki/ResponsesToPublicCommentsCR">
Responses to Public Comments on the Candidate Recommendation</a>
for more details about the justification of these changes.</p>
--- a/model/diff-n.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/diff-n.html Sun Apr 14 19:44:18 2013 +0200
@@ -895,7 +895,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and <span class="delete">Dublic</span><span class="insert">Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
--- a/model/diff.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/diff.html Sun Apr 14 19:44:18 2013 +0200
@@ -919,7 +919,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and <span class="delete">Dublic</span><span class="insert">Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
--- a/model/prov-constraints.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/prov-constraints.html Sun Apr 14 19:44:18 2013 +0200
@@ -848,7 +848,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [[PROV-DC]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [[PROV-DC]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
</ul>
@@ -1382,7 +1382,7 @@
</section>
<section id="overview" class="informative">
-<h4>Validation Process Overview</h4>
+<h2>Validation Process Overview</h2>
<p>
@@ -1407,13 +1407,13 @@
implementers, while the procedural approach adopted here immediately demonstrates
implementability and provides an adequate (polynomial-time) default implementation. In
this section we relate the declarative meaning of formulas to their
-procedural meaning. [[PROV-SEM]] will provide an alternative,
-declarative characterization of validity and equivalence which could
+procedural meaning. [[PROV-SEM]] provides an alternative,
+declarative characterization of validity which could
be used as a starting point for other implementation strategies. </p>
- <h4>Constants, Variables and Placeholders</h4>
+ <h3>Constants, Variables and Placeholders</h3>
<p>
PROV statements involve identifiers, literals,
placeholders, and attribute lists. Identifiers are, according to PROV-N, expressed as <a href="http://www.w3.org/TR/2013/REC-prov-n-20130430/#prod-QUALIFIED_NAME">qualified names</a> which can be mapped to URIs [[!RFC3987]].
@@ -1450,7 +1450,7 @@
</p>
- <h4>Substitution</h4>
+ <h3>Substitution</h3>
<p>A <em>substitution</em> is a function that maps variables to terms. Concretely, since we only
need to consider substitutions of finite sets of variables, we can
write substitutions as <span class="math">[x<sub>1</sub> = t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span>. A substitution
@@ -1482,7 +1482,7 @@
- <h4>Formulas</h4>
+ <h3>Formulas</h3>
<p>
For the purpose of constraint checking, we view PROV statements
(possibly involving existential variables) as
@@ -1497,7 +1497,7 @@
<li>Uniqueness constraints employ atomic equational formulas <span class="math">t =
t'</span>.</li>
<li>Ordering constraints employ atomic precedence relations that can
- be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math">strictly_precedes(t,t')</span>
+ be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math">strictlyPrecedes(t,t')</span>
</li>
<li>Typing constraints <span class="name">'type' ∈ typeOf(id)</span>
can be represented as a atomic formulas <span class="name">typeOf(id,'type')</span>.
@@ -1512,24 +1512,24 @@
background on logical formulas, see a logic textbook such as [[Logic]].</p>
<ul>
<li>
- A definition of the form <span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>
+ A definition of the form "<span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>"
can be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A ⇔ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the definition.
</li>
-<li>An inference of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span> can
+<li>An inference of the form "<span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>" can
be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the inference.
</li>
-<li>A uniqueness, ordering, or typing constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span> can be viewed as a formula
+<li>A uniqueness, ordering, or typing constraint of the form "<span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span>" can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ C</span>. </li>
-<li>A constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span> can be viewed as a formula
+<li>A constraint of the form "<span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span>" can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ False</span>. </li>
</ul>
- <h4>Satisfying definitions, inferences, and constraints</h4>
+ <h3>Satisfying definitions, inferences, and constraints</h3>
<p>
In logic, a formula's meaning is defined by saying when it is
<em>satisfied</em>. We can view
@@ -1548,7 +1548,7 @@
B<sub>k</sub></span> are either both true or both false.
</li>
<li>A logical implication as used in an inference is
- satisfied with the formula <span class="math">∀
+ satisfied when the formula <span class="math">∀
x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> holds, that is, for any substitution of
@@ -1569,7 +1569,7 @@
substitution for <span class="math">x<sub>1</sub>...x<sub>n</sub></span> making <span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> true.
</ol>
-<h4>Unification and Merging</h4>
+<h3>Unification and Merging</h3>
<p><em>Unification</em> is an operation that takes two terms and compares them to
determine whether they can be made equal by substituting an
@@ -1592,7 +1592,7 @@
- <h4>Applying definitions, inferences, and constraints</h4>
+ <h3>Applying definitions, inferences, and constraints</h3>
<p>Formulas can also be interpreted as having computational
content. That is, if an instance does not satisfy a formula, we can
often <em>apply</em> the formula to the instance to produce another
@@ -1621,7 +1621,7 @@
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> can be applied by searching for any occurrences of <span
class="math"> A<sub>1</sub> ∧ ... ∧
- A<sub>p</sub></span> in the instance and, for each such match,
+ A<sub>p</sub></span> in the instance and, for each such match
for which the entire conclusion does not already hold (for some <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>),
adding <span class="math">B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> to the instance, generating fresh existential
@@ -1668,7 +1668,7 @@
</p>
- <h4>Termination</h4>
+ <h3>Termination</h3>
<p>
In general, applying sets of logical formulas of the above
definition, inference, and constraint forms is not guaranteed to
@@ -1735,7 +1735,7 @@
</div>
- <h4>Checking ordering, typing, and impossibility constraints</h4>
+ <h3>Checking ordering, typing, and impossibility constraints</h3>
<p>
The ordering, typing, and impossibility constraints are checked
rather than applied. This means that they do not generate new
@@ -1801,7 +1801,7 @@
- <h4>Equivalence and Isomorphism</h4>
+ <h3>Equivalence and Isomorphism</h3>
<p> Given two normal forms, a natural question is whether they contain
the same information, that is, whether they are equivalent (if so,
then the original instances are also equivalent.) By analogy with
@@ -1858,7 +1858,7 @@
<li>every pair of invalid instances are equivalent</li>
</ol>
-<h4>From Instances to Bundles and Documents</h4>
+<h3>From Instances to Bundles and Documents</h3>
<p>PROV documents can contain multiple instances: a <a>toplevel
instance</a>, and
@@ -1888,7 +1888,7 @@
</section>
<section class="informative">
-<h4>Summary of inferences and constraints</h4>
+<h2>Summary of inferences and constraints</h2>
<p><a href="">Table 2</a> summarizes the inferences, and
constraints specified in this document, broken down by component and
@@ -2542,7 +2542,7 @@
<div class="remark">
- <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>TBD</span></a> and <a class="rule-ref" href="#optional-attributes"><span>TBD</span></a>.
+ <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>TBD</span></a> and <a class="rule-ref" href="#optional-attributes"><span>TBD</span></a>
do not apply to <span class="name">alternateOf</span> and <span class="name">specializationOf</span>, which do not have identifiers and attributes.
</p>
</div>
@@ -2722,7 +2722,7 @@
Essentially, the definitions state that parameters
<span class="name">g,u</span> are expandable only if the activity is specified, i.e., if parameter <span class="name">a</span> is provided.
-The rationale for this is that when a is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
+The rationale for this is that when <span class="name">a</span> is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
<p> A later constraint, <a class="rule-ref"
@@ -4562,7 +4562,7 @@
That is, <span class="name">typeOf(e)</span> returns the set of types
associated with identifier <span class="name">e</span>. The function
<span class="name">typeOf</span> is not a PROV statement, but a
-construct used only during validation PROV, similar to <a>precedes</a>.
+construct used only during validation, similar to <a>precedes</a>.
</p>
@@ -4982,11 +4982,8 @@
<a title="equivalence">equivalence</a> of PROV documents and instances. We first define these concepts
for PROV instances and then extend them to PROV documents.</p>
-<section id="instances">
- <h2>Instances</h2>
-
<div class="remark">
- Before normalization or validation, implementations should expand
+ Implementations should expand
namespace prefixes and perform any appropriate reasoning about
co-reference of identifiers, and rewrite the instance (by
replacing co-referent identifiers with a single common identifier) to
@@ -4998,6 +4995,10 @@
reasoning).
</div>
+ <section id="instances">
+ <h2>Instances</h2>
+
+
<p> We define the <dfn>normal form</dfn> of a PROV instance as the set
of provenance statements resulting from applying all definitions,
inferences, and uniqueness constraints, obtained as follows:</p>
@@ -5259,8 +5260,7 @@
attributes would also arise from one with no attributes.
</p>
- <p><b>Termination for instances without attributes.</b> For
- these instances, uniqueness and key constraints can be
+ <p><b>Termination for instances without attributes.</b>
As shown in [[DBCONSTRAINTS]], termination of normalization can be
shown by checking that the inference rules are <em>weakly
acyclic</em>. In addition, weak acyclicity can be checked
@@ -5389,13 +5389,20 @@
<ul>
<li> Changed the status of this document section.
<li> Changed all URLs to PROV documents.
+ <li> Fixed some minor typos in section 2.4.
+ <li> Fixed typo in remark after definition 2.
+ <li> Fixed typo in paragraph after table 2.
+ <li> Fixed typo in sec. 6.3.
+ <li> Fixed wording in remark in sec. 7.1, and moved it before
+ section heading.
+ <li> Fixed typo in appendix A.
</ul>
</section>
<section class="appendix">
- <h2>Changes from Candidate Recommendation to this version</h2>
+ <h2>Changes from Candidate Recommendation to Proposed Recommendation</h2>
<p> Please see the <a
href="http://www.w3.org/2011/prov/wiki/ResponsesToPublicCommentsCR">
Responses to Public Comments on the Candidate Recommendation</a>
--- a/model/prov-dm.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/prov-dm.html Sun Apr 14 19:44:18 2013 +0200
@@ -869,7 +869,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [[PROV-DC]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [[PROV-DC]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
</ul>
--- a/model/prov-n.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/prov-n.html Sun Apr 14 19:44:18 2013 +0200
@@ -833,7 +833,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [[PROV-DC]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [[PROV-DC]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
</ul>
--- a/model/releases/REC-prov-constraints-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/releases/REC-prov-constraints-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -802,7 +802,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
@@ -852,7 +852,7 @@
</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1. </span>Introduction<br>
-</a><ul class="toc"><li class="tocline"><a href="#conventions" class="tocxref"><span class="secno">1.1 </span>Conventions</a></li><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.2 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.3 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.4 </span> Audience </a></li></ul></li><li class="tocline"><a href="#rationale" class="tocxref"><span class="secno">2. </span>Rationale (Informative)</a><ul class="toc"><li class="tocline"><a href="#entities-activities-and-agents" class="tocxref"><span class="secno">2.1 </span>Entities, Activities and Agents</a></li><li class="tocline"><a href="#events" class="tocxref"><span class="secno">2.2 </span>Events</a></li><li class="tocline"><a href="#typing-section" class="tocxref"><span class="secno">2.3 </span>Types</a></li><li class="tocline"><a href="#overview" class="tocxref"><span class="secno">2.4 </span>Validation Process Overview</a></li><li class="tocline"><a href="#summary-of-inferences-and-constraints" class="tocxref"><span class="secno">2.5 </span>Summary of inferences and constraints</a></li></ul></li><li class="tocline"><a href="#compliance" class="tocxref"><span class="secno">3. </span>Compliance with this document</a></li><li class="tocline"><a href="#concepts" class="tocxref"><span class="secno">4. </span>Basic concepts</a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5. </span>Definitions and Inferences</a><ul class="toc"><li class="tocline"><a href="#optional-identifiers-and-attributes" class="tocxref"><span class="secno">5.1 </span>Optional Identifiers and Attributes</a></li><li class="tocline"><a href="#entities-and-activities" class="tocxref"><span class="secno">5.2 </span>Entities and Activities</a></li><li class="tocline"><a href="#derivations" class="tocxref"><span class="secno">5.3 </span>Derivations</a></li><li class="tocline"><a href="#agents" class="tocxref"><span class="secno">5.4 </span>Agents</a></li><li class="tocline"><a href="#alternate-and-specialized-entities" class="tocxref"><span class="secno">5.5 </span>Alternate and Specialized Entities</a></li></ul></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">6. </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">6.1 </span>Uniqueness Constraints</a></li><li class="tocline"><a href="#event-ordering-constraints" class="tocxref"><span class="secno">6.2 </span>Event Ordering Constraints</a><ul class="toc"><li class="tocline"><a href="#activity-constraints" class="tocxref"><span class="secno">6.2.1 </span>Activity constraints</a></li><li class="tocline"><a href="#entity-constraints" class="tocxref"><span class="secno">6.2.2 </span> Entity constraints</a></li><li class="tocline"><a href="#agent-constraints" class="tocxref"><span class="secno">6.2.3 </span> Agent constraints</a></li></ul></li><li class="tocline"><a href="#type-constraints" class="tocxref"><span class="secno">6.3 </span>Type Constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">6.4 </span>Impossibility constraints</a></li></ul></li><li class="tocline"><a href="#normalization-validity-equivalence" class="tocxref"><span class="secno">7. </span>Normalization, Validity, and Equivalence</a><ul class="toc"><li class="tocline"><a href="#instances" class="tocxref"><span class="secno">7.1 </span>Instances</a></li><li class="tocline"><a href="#bundle-constraints" class="tocxref"><span class="secno">7.2 </span>Bundles and Documents</a></li></ul></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno">8. </span>Glossary</a></li><li class="tocline"><a href="#termination" class="tocxref"><span class="secno">A. </span>Termination of normalization</a></li><li class="tocline"><a href="#change-log" class="tocxref"><span class="secno">B. </span>Change Log</a><ul class="toc"><li class="tocline"><a href="#changes-since-proposed-recommendation" class="tocxref"><span class="secno">B.1 </span>Changes since Proposed Recommendation</a></li><li class="tocline"><a href="#changes-from-candidate-recommendation-to-this-version" class="tocxref"><span class="secno">B.2 </span>Changes from Candidate Recommendation to this version</a></li><li class="tocline"><a href="#changes-from-last-call-working-draft-to-candidate-recommendation" class="tocxref"><span class="secno">B.3 </span>Changes from Last Call Working Draft to Candidate Recommendation</a></li></ul></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">C. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">D. </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">D.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">D.2 </span>Informative references</a></li></ul></li></ul></section>
+</a><ul class="toc"><li class="tocline"><a href="#conventions" class="tocxref"><span class="secno">1.1 </span>Conventions</a></li><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.2 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.3 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.4 </span> Audience </a></li></ul></li><li class="tocline"><a href="#rationale" class="tocxref"><span class="secno">2. </span>Rationale (Informative)</a><ul class="toc"><li class="tocline"><a href="#entities-activities-and-agents" class="tocxref"><span class="secno">2.1 </span>Entities, Activities and Agents</a></li><li class="tocline"><a href="#events" class="tocxref"><span class="secno">2.2 </span>Events</a></li><li class="tocline"><a href="#typing-section" class="tocxref"><span class="secno">2.3 </span>Types</a></li><li class="tocline"><a href="#overview" class="tocxref"><span class="secno">2.4 </span>Validation Process Overview</a></li><li class="tocline"><a href="#summary-of-inferences-and-constraints" class="tocxref"><span class="secno">2.5 </span>Summary of inferences and constraints</a></li></ul></li><li class="tocline"><a href="#compliance" class="tocxref"><span class="secno">3. </span>Compliance with this document</a></li><li class="tocline"><a href="#concepts" class="tocxref"><span class="secno">4. </span>Basic concepts</a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5. </span>Definitions and Inferences</a><ul class="toc"><li class="tocline"><a href="#optional-identifiers-and-attributes" class="tocxref"><span class="secno">5.1 </span>Optional Identifiers and Attributes</a></li><li class="tocline"><a href="#entities-and-activities" class="tocxref"><span class="secno">5.2 </span>Entities and Activities</a></li><li class="tocline"><a href="#derivations" class="tocxref"><span class="secno">5.3 </span>Derivations</a></li><li class="tocline"><a href="#agents" class="tocxref"><span class="secno">5.4 </span>Agents</a></li><li class="tocline"><a href="#alternate-and-specialized-entities" class="tocxref"><span class="secno">5.5 </span>Alternate and Specialized Entities</a></li></ul></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">6. </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">6.1 </span>Uniqueness Constraints</a></li><li class="tocline"><a href="#event-ordering-constraints" class="tocxref"><span class="secno">6.2 </span>Event Ordering Constraints</a><ul class="toc"><li class="tocline"><a href="#activity-constraints" class="tocxref"><span class="secno">6.2.1 </span>Activity constraints</a></li><li class="tocline"><a href="#entity-constraints" class="tocxref"><span class="secno">6.2.2 </span> Entity constraints</a></li><li class="tocline"><a href="#agent-constraints" class="tocxref"><span class="secno">6.2.3 </span> Agent constraints</a></li></ul></li><li class="tocline"><a href="#type-constraints" class="tocxref"><span class="secno">6.3 </span>Type Constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">6.4 </span>Impossibility constraints</a></li></ul></li><li class="tocline"><a href="#normalization-validity-equivalence" class="tocxref"><span class="secno">7. </span>Normalization, Validity, and Equivalence</a><ul class="toc"><li class="tocline"><a href="#instances" class="tocxref"><span class="secno">7.1 </span>Instances</a></li><li class="tocline"><a href="#bundle-constraints" class="tocxref"><span class="secno">7.2 </span>Bundles and Documents</a></li></ul></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno">8. </span>Glossary</a></li><li class="tocline"><a href="#termination" class="tocxref"><span class="secno">A. </span>Termination of normalization</a></li><li class="tocline"><a href="#change-log" class="tocxref"><span class="secno">B. </span>Change Log</a><ul class="toc"><li class="tocline"><a href="#changes-since-proposed-recommendation" class="tocxref"><span class="secno">B.1 </span>Changes since Proposed Recommendation</a></li><li class="tocline"><a href="#changes-from-candidate-recommendation-to-proposed-recommendation" class="tocxref"><span class="secno">B.2 </span>Changes from Candidate Recommendation to Proposed Recommendation</a></li><li class="tocline"><a href="#changes-from-last-call-working-draft-to-candidate-recommendation" class="tocxref"><span class="secno">B.3 </span>Changes from Last Call Working Draft to Candidate Recommendation</a></li></ul></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">C. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">D. </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">D.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">D.2 </span>Informative references</a></li></ul></li></ul></section>
@@ -1398,8 +1398,8 @@
implementers, while the procedural approach adopted here immediately demonstrates
implementability and provides an adequate (polynomial-time) default implementation. In
this section we relate the declarative meaning of formulas to their
-procedural meaning. [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>] will provide an alternative,
-declarative characterization of validity and equivalence which could
+procedural meaning. [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>] provides an alternative,
+declarative characterization of validity which could
be used as a starting point for other implementation strategies. </p>
@@ -1441,7 +1441,7 @@
</p>
- <h4 id="substitution-1">Substitution</h4><p><em>This section is non-normative.</em></p>
+ <h3 id="substitution-1">Substitution</h3>
<p>A <em>substitution</em> is a function that maps variables to terms. Concretely, since we only
need to consider substitutions of finite sets of variables, we can
write substitutions as <span class="math">[x<sub>1</sub> = t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span>. A substitution
@@ -1473,7 +1473,7 @@
- <h4 id="formulas">Formulas</h4>
+ <h3 id="formulas">Formulas</h3>
<p>
For the purpose of constraint checking, we view PROV statements
(possibly involving existential variables) as
@@ -1488,7 +1488,7 @@
<li>Uniqueness constraints employ atomic equational formulas <span class="math">t =
t'</span>.</li>
<li>Ordering constraints employ atomic precedence relations that can
- be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math">strictly_precedes(t,t')</span>
+ be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math">strictlyPrecedes(t,t')</span>
</li>
<li>Typing constraints <span class="name">'type' ∈ typeOf(id)</span>
can be represented as a atomic formulas <span class="name">typeOf(id,'type')</span>.
@@ -1503,24 +1503,24 @@
background on logical formulas, see a logic textbook such as [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>].</p>
<ul>
<li>
- A definition of the form <span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>
+ A definition of the form "<span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>"
can be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A ⇔ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the definition.
</li>
-<li>An inference of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span> can
+<li>An inference of the form "<span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>" can
be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the inference.
</li>
-<li>A uniqueness, ordering, or typing constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span> can be viewed as a formula
+<li>A uniqueness, ordering, or typing constraint of the form "<span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span>" can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ C</span>. </li>
-<li>A constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span> can be viewed as a formula
+<li>A constraint of the form "<span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span>" can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ False</span>. </li>
</ul>
- <h4 id="satisfying-definitions-inferences-and-constraints">Satisfying definitions, inferences, and constraints</h4>
+ <h3 id="satisfying-definitions-inferences-and-constraints">Satisfying definitions, inferences, and constraints</h3>
<p>
In logic, a formula's meaning is defined by saying when it is
<em>satisfied</em>. We can view
@@ -1539,7 +1539,7 @@
B<sub>k</sub></span> are either both true or both false.
</li>
<li>A logical implication as used in an inference is
- satisfied with the formula <span class="math">∀
+ satisfied when the formula <span class="math">∀
x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> holds, that is, for any substitution of
@@ -1560,7 +1560,7 @@
substitution for <span class="math">x<sub>1</sub>...x<sub>n</sub></span> making <span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> true.
</li></ol>
-<h4 id="unification-and-merging">Unification and Merging</h4>
+<h3 id="unification-and-merging">Unification and Merging</h3>
<p><em>Unification</em> is an operation that takes two terms and compares them to
determine whether they can be made equal by substituting an
@@ -1583,7 +1583,7 @@
- <h4 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h4>
+ <h3 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h3>
<p>Formulas can also be interpreted as having computational
content. That is, if an instance does not satisfy a formula, we can
often <em>apply</em> the formula to the instance to produce another
@@ -1609,7 +1609,7 @@
x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> can be applied by searching for any occurrences of <span class="math"> A<sub>1</sub> ∧ ... ∧
- A<sub>p</sub></span> in the instance and, for each such match,
+ A<sub>p</sub></span> in the instance and, for each such match
for which the entire conclusion does not already hold (for some <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>),
adding <span class="math">B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> to the instance, generating fresh existential
@@ -1656,7 +1656,7 @@
</p>
- <h4 id="termination-1">Termination</h4>
+ <h3 id="termination-1">Termination</h3>
<p>
In general, applying sets of logical formulas of the above
definition, inference, and constraint forms is not guaranteed to
@@ -1719,7 +1719,7 @@
</div>
- <h4 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h4>
+ <h3 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h3>
<p>
The ordering, typing, and impossibility constraints are checked
rather than applied. This means that they do not generate new
@@ -1785,7 +1785,7 @@
- <h4 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h4>
+ <h3 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h3>
<p> Given two normal forms, a natural question is whether they contain
the same information, that is, whether they are equivalent (if so,
then the original instances are also equivalent.) By analogy with
@@ -1842,7 +1842,7 @@
<li>every pair of invalid instances are equivalent</li>
</ol>
-<h4 id="from-instances-to-bundles-and-documents">From Instances to Bundles and Documents</h4>
+<h3 id="from-instances-to-bundles-and-documents">From Instances to Bundles and Documents</h3>
<p>PROV documents can contain multiple instances: a <a href="#dfn-toplevel-instance" class="internalDFN">toplevel
instance</a>, and
@@ -2498,7 +2498,7 @@
<div class="remark">
- <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a> and <a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a>.
+ <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a> and <a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a>
do not apply to <span class="name">alternateOf</span> and <span class="name">specializationOf</span>, which do not have identifiers and attributes.
</p>
</div>
@@ -2670,7 +2670,7 @@
Essentially, the definitions state that parameters
<span class="name">g,u</span> are expandable only if the activity is specified, i.e., if parameter <span class="name">a</span> is provided.
-The rationale for this is that when a is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
+The rationale for this is that when <span class="name">a</span> is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
<p> A later constraint, <a class="rule-ref" href="#impossible-unspecified-derivation-generation-use"><span>Constraint 51 (impossible-unspecified-derivation-generation-use)</span></a>,
@@ -4405,7 +4405,7 @@
That is, <span class="name">typeOf(e)</span> returns the set of types
associated with identifier <span class="name">e</span>. The function
<span class="name">typeOf</span> is not a PROV statement, but a
-construct used only during validation PROV, similar to <a href="#dfn-precedes" class="internalDFN">precedes</a>.
+construct used only during validation, similar to <a href="#dfn-precedes" class="internalDFN">precedes</a>.
</p>
@@ -4809,11 +4809,8 @@
<a title="equivalence">equivalence</a> of PROV documents and instances. We first define these concepts
for PROV instances and then extend them to PROV documents.</p>
-<section id="instances">
- <h3><span class="secno">7.1 </span>Instances</h3>
-
<div class="remark">
- Before normalization or validation, implementations should expand
+ Implementations should expand
namespace prefixes and perform any appropriate reasoning about
co-reference of identifiers, and rewrite the instance (by
replacing co-referent identifiers with a single common identifier) to
@@ -4825,6 +4822,10 @@
reasoning).
</div>
+ <section id="instances">
+ <h3><span class="secno">7.1 </span>Instances</h3>
+
+
<p> We define the <dfn id="dfn-normal-form">normal form</dfn> of a PROV instance as the set
of provenance statements resulting from applying all definitions,
inferences, and uniqueness constraints, obtained as follows:</p>
@@ -5082,8 +5083,7 @@
attributes would also arise from one with no attributes.
</p>
- <p><b>Termination for instances without attributes.</b> For
- these instances, uniqueness and key constraints can be
+ <p><b>Termination for instances without attributes.</b>
As shown in [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>], termination of normalization can be
shown by checking that the inference rules are <em>weakly
acyclic</em>. In addition, weak acyclicity can be checked
@@ -5211,13 +5211,20 @@
<ul>
<li> Changed the status of this document section.
</li><li> Changed all URLs to PROV documents.
+ </li><li> Fixed some minor typos in section 2.4.
+ </li><li> Fixed typo in remark after definition 2.
+ </li><li> Fixed typo in paragraph after table 2.
+ </li><li> Fixed typo in sec. 6.3.
+ </li><li> Fixed wording in remark in sec. 7.1, and moved it before
+ section heading.
+ </li><li> Fixed typo in appendix A.
</li></ul>
</section>
-<section class="appendix" id="changes-from-candidate-recommendation-to-this-version">
- <h3><span class="secno">B.2 </span>Changes from Candidate Recommendation to this version</h3>
+<section class="appendix" id="changes-from-candidate-recommendation-to-proposed-recommendation">
+ <h3><span class="secno">B.2 </span>Changes from Candidate Recommendation to Proposed Recommendation</h3>
<p> Please see the <a href="http://www.w3.org/2011/prov/wiki/ResponsesToPublicCommentsCR">
Responses to Public Comments on the Candidate Recommendation</a>
for more details about the justification of these changes.</p>
--- a/model/releases/REC-prov-constraints-20130430/diff-c.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/releases/REC-prov-constraints-20130430/diff-c.html Sun Apr 14 19:44:18 2013 +0200
@@ -815,7 +815,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV and Dublic</span><span class="insert">PROV-O and Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
@@ -902,7 +902,7 @@
</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1. </span>Introduction<br>
-</a><ul class="toc"><li class="tocline"><a href="#conventions" class="tocxref"><span class="secno">1.1 </span>Conventions</a></li><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.2 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.3 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.4 </span> Audience </a></li></ul></li><li class="tocline"><a href="#rationale" class="tocxref"><span class="secno">2. </span>Rationale (Informative)</a><ul class="toc"><li class="tocline"><a href="#entities-activities-and-agents" class="tocxref"><span class="secno">2.1 </span>Entities, Activities and Agents</a></li><li class="tocline"><a href="#events" class="tocxref"><span class="secno">2.2 </span>Events</a></li><li class="tocline"><a href="#typing-section" class="tocxref"><span class="secno">2.3 </span>Types</a></li><li class="tocline"><a href="#overview" class="tocxref"><span class="secno">2.4 </span>Validation Process Overview</a></li><li class="tocline"><a href="#summary-of-inferences-and-constraints" class="tocxref"><span class="secno">2.5 </span>Summary of inferences and constraints</a></li></ul></li><li class="tocline"><a href="#compliance" class="tocxref"><span class="secno">3. </span>Compliance with this document</a></li><li class="tocline"><a href="#concepts" class="tocxref"><span class="secno">4. </span>Basic concepts</a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5. </span>Definitions and Inferences</a><ul class="toc"><li class="tocline"><a href="#optional-identifiers-and-attributes" class="tocxref"><span class="secno">5.1 </span>Optional Identifiers and Attributes</a></li><li class="tocline"><a href="#entities-and-activities" class="tocxref"><span class="secno">5.2 </span>Entities and Activities</a></li><li class="tocline"><a href="#derivations" class="tocxref"><span class="secno">5.3 </span>Derivations</a></li><li class="tocline"><a href="#agents" class="tocxref"><span class="secno">5.4 </span>Agents</a></li><li class="tocline"><a href="#alternate-and-specialized-entities" class="tocxref"><span class="secno">5.5 </span>Alternate and Specialized Entities</a></li></ul></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">6. </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">6.1 </span>Uniqueness Constraints</a></li><li class="tocline"><a href="#event-ordering-constraints" class="tocxref"><span class="secno">6.2 </span>Event Ordering Constraints</a><ul class="toc"><li class="tocline"><a href="#activity-constraints" class="tocxref"><span class="secno">6.2.1 </span>Activity constraints</a></li><li class="tocline"><a href="#entity-constraints" class="tocxref"><span class="secno">6.2.2 </span> Entity constraints</a></li><li class="tocline"><a href="#agent-constraints" class="tocxref"><span class="secno">6.2.3 </span> Agent constraints</a></li></ul></li><li class="tocline"><a href="#type-constraints" class="tocxref"><span class="secno">6.3 </span>Type Constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">6.4 </span>Impossibility constraints</a></li></ul></li><li class="tocline"><a href="#normalization-validity-equivalence" class="tocxref"><span class="secno">7. </span>Normalization, Validity, and Equivalence</a><ul class="toc"><li class="tocline"><a href="#instances" class="tocxref"><span class="secno">7.1 </span>Instances</a></li><li class="tocline"><a href="#bundle-constraints" class="tocxref"><span class="secno">7.2 </span>Bundles and Documents</a></li></ul></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno">8. </span>Glossary</a></li><li class="tocline"><a href="#termination" class="tocxref"><span class="secno">A. </span>Termination of normalization</a></li><li class="tocline"><a href="#change-log" class="tocxref"><span class="secno">B. </span>Change Log</a><ul class="toc"><li class="tocline"><a href="#changes-since-proposed-recommendation" class="tocxref"><span class="secno"><span class="insert">B.1 </span></span><span class="insert">Changes since Proposed Recommendation</span></a></li><li class="tocline"><a href="#changes-from-candidate-recommendation-to-this-version" class="tocxref"><span class="secno"><span class="delete">B.1</span><span class="insert">B.2</span> </span>Changes from Candidate Recommendation to this version</a></li><li class="tocline"><a href="#changes-from-last-call-working-draft-to-candidate-recommendation" class="tocxref"><span class="secno"><span class="delete">B.2</span><span class="insert">B.3</span> </span>Changes from Last Call Working Draft to Candidate Recommendation</a></li></ul></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">C. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">D. </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">D.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">D.2 </span>Informative references</a></li></ul></li></ul></section>
+</a><ul class="toc"><li class="tocline"><a href="#conventions" class="tocxref"><span class="secno">1.1 </span>Conventions</a></li><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.2 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.3 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.4 </span> Audience </a></li></ul></li><li class="tocline"><a href="#rationale" class="tocxref"><span class="secno">2. </span>Rationale (Informative)</a><ul class="toc"><li class="tocline"><a href="#entities-activities-and-agents" class="tocxref"><span class="secno">2.1 </span>Entities, Activities and Agents</a></li><li class="tocline"><a href="#events" class="tocxref"><span class="secno">2.2 </span>Events</a></li><li class="tocline"><a href="#typing-section" class="tocxref"><span class="secno">2.3 </span>Types</a></li><li class="tocline"><a href="#overview" class="tocxref"><span class="secno">2.4 </span>Validation Process Overview</a></li><li class="tocline"><a href="#summary-of-inferences-and-constraints" class="tocxref"><span class="secno">2.5 </span>Summary of inferences and constraints</a></li></ul></li><li class="tocline"><a href="#compliance" class="tocxref"><span class="secno">3. </span>Compliance with this document</a></li><li class="tocline"><a href="#concepts" class="tocxref"><span class="secno">4. </span>Basic concepts</a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5. </span>Definitions and Inferences</a><ul class="toc"><li class="tocline"><a href="#optional-identifiers-and-attributes" class="tocxref"><span class="secno">5.1 </span>Optional Identifiers and Attributes</a></li><li class="tocline"><a href="#entities-and-activities" class="tocxref"><span class="secno">5.2 </span>Entities and Activities</a></li><li class="tocline"><a href="#derivations" class="tocxref"><span class="secno">5.3 </span>Derivations</a></li><li class="tocline"><a href="#agents" class="tocxref"><span class="secno">5.4 </span>Agents</a></li><li class="tocline"><a href="#alternate-and-specialized-entities" class="tocxref"><span class="secno">5.5 </span>Alternate and Specialized Entities</a></li></ul></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">6. </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">6.1 </span>Uniqueness Constraints</a></li><li class="tocline"><a href="#event-ordering-constraints" class="tocxref"><span class="secno">6.2 </span>Event Ordering Constraints</a><ul class="toc"><li class="tocline"><a href="#activity-constraints" class="tocxref"><span class="secno">6.2.1 </span>Activity constraints</a></li><li class="tocline"><a href="#entity-constraints" class="tocxref"><span class="secno">6.2.2 </span> Entity constraints</a></li><li class="tocline"><a href="#agent-constraints" class="tocxref"><span class="secno">6.2.3 </span> Agent constraints</a></li></ul></li><li class="tocline"><a href="#type-constraints" class="tocxref"><span class="secno">6.3 </span>Type Constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">6.4 </span>Impossibility constraints</a></li></ul></li><li class="tocline"><a href="#normalization-validity-equivalence" class="tocxref"><span class="secno">7. </span>Normalization, Validity, and Equivalence</a><ul class="toc"><li class="tocline"><a href="#instances" class="tocxref"><span class="secno">7.1 </span>Instances</a></li><li class="tocline"><a href="#bundle-constraints" class="tocxref"><span class="secno">7.2 </span>Bundles and Documents</a></li></ul></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno">8. </span>Glossary</a></li><li class="tocline"><a href="#termination" class="tocxref"><span class="secno">A. </span>Termination of normalization</a></li><li class="tocline"><a href="#change-log" class="tocxref"><span class="secno">B. </span>Change Log</a><ul class="toc"><li class="tocline"><a href="#changes-since-proposed-recommendation" class="tocxref"><span class="secno">B.1 </span>Changes <span class="insert">since Proposed Recommendation</span></a></li><li class="tocline"><a href="#changes-from-candidate-recommendation-to-proposed-recommendation" class="tocxref"><span class="secno"><span class="insert">B.2 </span></span><span class="insert">Changes </span>from Candidate Recommendation to <span class="delete">this version</span><span class="insert">Proposed Recommendation</span></a></li><li class="tocline"><a href="#changes-from-last-call-working-draft-to-candidate-recommendation" class="tocxref"><span class="secno"><span class="delete">B.2</span><span class="insert">B.3</span> </span>Changes from Last Call Working Draft to Candidate Recommendation</a></li></ul></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">C. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">D. </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">D.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">D.2 </span>Informative references</a></li></ul></li></ul></section>
@@ -1434,8 +1434,8 @@
implementers, while the procedural approach adopted here immediately demonstrates
implementability and provides an adequate (polynomial-time) default implementation. In
this section we relate the declarative meaning of formulas to their
-procedural meaning. [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>] will provide an alternative,
-declarative characterization of validity and equivalence which could
+procedural meaning. [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>] <span class="delete">will provide</span><span class="insert">provides</span> an alternative,
+declarative characterization of validity<span class="delete"> and equivalence</span> which could
be used as a starting point for other implementation strategies. </p>
@@ -1477,7 +1477,7 @@
</p>
- <h4 id="substitution-1">Substitution</h4><p><em>This section is non-normative.</em></p>
+ <h3 id="substitution-1">Substitution<span class="delete">This section is non-normative.</span></h3>
<p>A <em>substitution</em> is a function that maps variables to terms. Concretely, since we only
need to consider substitutions of finite sets of variables, we can
write substitutions as <span class="math">[x<sub>1</sub> = t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span>. A substitution
@@ -1499,7 +1499,7 @@
- <h4 id="formulas">Formulas</h4>
+ <h3 id="formulas">Formulas</h3>
<p>
For the purpose of constraint checking, we view PROV statements
(possibly involving existential variables) as
@@ -1514,7 +1514,7 @@
<li>Uniqueness constraints employ atomic equational formulas <span class="math">t =
t'</span>.</li>
<li>Ordering constraints employ atomic precedence relations that can
- be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math">strictly_precedes(t,t')</span>
+ be thought of as binary formulas <span class="math">precedes(t,t')</span> or <span class="math"><span class="delete">strictly_precedes(t,t')</span><span class="insert">strictlyPrecedes(t,t')</span></span>
</li>
<li>Typing constraints <span class="name">'type' ∈ typeOf(id)</span>
can be represented as a atomic formulas <span class="name">typeOf(id,'type')</span>.
@@ -1529,24 +1529,24 @@
background on logical formulas, see a logic textbook such as [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>].</p>
<ul>
<li>
- A definition of the form <span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span>
+ A definition of the form <span class="insert">"</span><span class="name">A</span> <span class="conditional">IF AND ONLY IF</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span><span class="insert">"</span>
can be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A ⇔ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the definition.
</li>
-<li>An inference of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
- exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span> can
+<li>An inference of the form <span class="insert">"</span><span class="conditional">IF</span> <span class="name">A<sub>1</sub></span> and ... and <span class="name">A<sub>p</sub></span> <span class="conditional">THEN</span> there
+ exists <span class="name">y<sub>1</sub></span>...<span class="name">y<sub>m</sub></span> such that <span class="name">B<sub>1</sub></span> and ... and <span class="name">B<sub>k</sub></span><span class="insert">"</span> can
be thought of as a formula <span class="math">∀ x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧ ... ∧ B<sub>k</sub></span>, where <span class="math">x<sub>1</sub></span>...<span class="math">x<sub>n</sub></span> are the
free variables of the inference.
</li>
-<li>A uniqueness, ordering, or typing constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span> can be viewed as a formula
+<li>A uniqueness, ordering, or typing constraint of the form <span class="insert">"</span><span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN</span> <span class="name">C</span><span class="insert">"</span> can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ C</span>. </li>
-<li>A constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span> can be viewed as a formula
+<li>A constraint of the form <span class="insert">"</span><span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> <span class="conditional">THEN INVALID</span><span class="insert">"</span> can be viewed as a formula
<span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ False</span>. </li>
</ul>
- <h4 id="satisfying-definitions-inferences-and-constraints">Satisfying definitions, inferences, and constraints</h4>
+ <h3 id="satisfying-definitions-inferences-and-constraints">Satisfying definitions, inferences, and constraints</h3>
<p>
In logic, a formula's meaning is defined by saying when it is
<em>satisfied</em>. We can view
@@ -1565,7 +1565,7 @@
B<sub>k</sub></span> are either both true or both false.
</li>
<li>A logical implication as used in an inference is
- satisfied with the formula <span class="math">∀
+ satisfied <span class="delete">with</span><span class="insert">when</span> the formula <span class="math">∀
x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> holds, that is, for any substitution of
@@ -1586,7 +1586,7 @@
substitution for <span class="math">x<sub>1</sub>...x<sub>n</sub></span> making <span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> true.
</li></ol>
-<h4 id="unification-and-merging">Unification and Merging</h4>
+<h3 id="unification-and-merging">Unification and Merging</h3>
<p><em>Unification</em> is an operation that takes two terms and compares them to
determine whether they can be made equal by substituting an
@@ -1609,7 +1609,7 @@
- <h4 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h4>
+ <h3 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h3>
<p>Formulas can also be interpreted as having computational
content. That is, if an instance does not satisfy a formula, we can
often <em>apply</em> the formula to the instance to produce another
@@ -1635,7 +1635,7 @@
x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
A<sub>p</sub> ⇒ ∃ y<sub>1</sub>...y<sub>m</sub> . B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> can be applied by searching for any occurrences of <span class="math"> A<sub>1</sub> ∧ ... ∧
- A<sub>p</sub></span> in the instance and, for each such match,
+ A<sub>p</sub></span> in the instance and, for each such <span class="delete">match,</span><span class="insert">match</span>
for which the entire conclusion does not already hold (for some <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>),
adding <span class="math">B<sub>1</sub> ∧
... ∧ B<sub>k</sub></span> to the instance, generating fresh existential
@@ -1682,7 +1682,7 @@
</p>
- <h4 id="termination-1">Termination</h4>
+ <h3 id="termination-1">Termination</h3>
<p>
In general, applying sets of logical formulas of the above
definition, inference, and constraint forms is not guaranteed to
@@ -1745,7 +1745,7 @@
</div>
- <h4 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h4>
+ <h3 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h3>
<p>
The ordering, typing, and impossibility constraints are checked
rather than applied. This means that they do not generate new
@@ -1811,7 +1811,7 @@
- <h4 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h4>
+ <h3 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h3>
<p> Given two normal forms, a natural question is whether they contain
the same information, that is, whether they are equivalent (if so,
then the original instances are also equivalent.) By analogy with
@@ -1865,7 +1865,7 @@
<li>every pair of invalid instances are equivalent</li>
</ol>
-<h4 id="from-instances-to-bundles-and-documents">From Instances to Bundles and Documents</h4>
+<h3 id="from-instances-to-bundles-and-documents">From Instances to Bundles and Documents</h3>
<p>PROV documents can contain multiple instances: a <a href="#dfn-toplevel-instance" class="internalDFN">toplevel
instance</a>, and
@@ -2501,7 +2501,8 @@
<div class="remark">
- <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a> and <a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a>.
+ <p>Definitions <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a> and <a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a><span class="delete">.
+</span>
do not apply to <span class="name">alternateOf</span> and <span class="name">specializationOf</span>, which do not have identifiers and attributes.
</p>
</div>
@@ -2643,7 +2644,7 @@
Essentially, the definitions state that parameters
<span class="name">g,u</span> are expandable only if the activity is specified, i.e., if parameter <span class="name">a</span> is provided.
-The rationale for this is that when a is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
+The rationale for this is that when <span class="name">a</span> is provided, then there have to be two events, namely <span class="name">u</span> and <span class="name">g</span>, which account for the usage of <span class="name">e1</span> and the generation of <span class="name">e2</span>, respectively, by <span class="name">a</span>. Conversely, if <span class="name">a</span> is not provided, then one cannot tell whether one or more activities are involved in the derivation, and the explicit introduction of such events, which correspond to a single activity, would therefore not be justified. </p>
<p> A later constraint, <a class="rule-ref" href="#impossible-unspecified-derivation-generation-use"><span>Constraint 51 (impossible-unspecified-derivation-generation-use)</span></a>,
@@ -4145,7 +4146,7 @@
That is, <span class="name">typeOf(e)</span> returns the set of types
associated with identifier <span class="name">e</span>. The function
<span class="name">typeOf</span> is not a PROV statement, but a
-construct used only during validation PROV, similar to <a href="#dfn-precedes" class="internalDFN">precedes</a>.
+construct used only during <span class="delete">validation PROV,</span><span class="insert">validation,</span> similar to <a href="#dfn-precedes" class="internalDFN">precedes</a>.
</p>
@@ -4521,10 +4522,23 @@
<a title="equivalence">equivalence</a> of PROV documents and instances. We first define these concepts
for PROV instances and then extend them to PROV documents.</p>
-<section id="instances">
+<div class="remark"><span class="insert">
+ Implementations should expand
+ namespace prefixes and perform any appropriate reasoning about
+ co-reference of identifiers, and rewrite the instance (by
+ replacing co-referent identifiers with a single common identifier) to
+ make this explicit, before doing validation, equivalence checking,
+ or normalization.
+ All of the following definitions assume that the application has
+ already determined which URIs in the PROV instance are co-referent
+ (e.g. </span><span class="name"><span class="insert">owl:sameAs</span></span><span class="insert"> as a result of OWL
+ reasoning).
+ </span></div>
+
+ <section id="instances">
<h3><span class="secno">7.1 </span>Instances</h3>
-<div class="remark">
+<span class="delete">
Before normalization or validation, implementations should expand
namespace prefixes and perform any appropriate reasoning about
co-reference of identifiers, and rewrite the instance (by
@@ -4533,9 +4547,12 @@
or normalization.
All of the following definitions assume that the application has
already determined which URIs in the PROV instance are co-referent
- (e.g. <span class="name">owl:sameAs</span> as a result of OWL
+ (e.g. </span><span class="delete">owl:sameAs</span><span class="delete"> as a result of OWL
reasoning).
- </div>
+ </span>
+
+
+
<p> We define the <dfn id="dfn-normal-form">normal form</dfn> of a PROV instance as the set
of provenance statements resulting from applying all definitions,
@@ -4794,8 +4811,9 @@
attributes would also arise from one with no attributes.
</p>
- <p><b>Termination for instances without attributes.</b> For
+ <p><b>Termination for instances without attributes.</b><span class="delete"> For
these instances, uniqueness and key constraints can be
+ </span>
As shown in [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>], termination of normalization can be
shown by checking that the inference rules are <em>weakly
acyclic</em>. In addition, weak acyclicity can be checked
@@ -4923,13 +4941,20 @@
<ul>
<li><span class="insert"> Changed the status of this document section.
</span></li><li><span class="insert"> Changed all URLs to PROV documents.
+ </span></li><li><span class="insert"> Fixed some minor typos in section 2.4.
+ </span></li><li><span class="insert"> Fixed typo in remark after definition 2.
+ </span></li><li><span class="insert"> Fixed typo in paragraph after table 2.
+ </span></li><li><span class="insert"> Fixed typo in sec. 6.3.
+ </span></li><li><span class="insert"> Fixed wording in remark in sec. 7.1, and moved it before
+ section heading.
+ </span></li><li><span class="insert"> Fixed typo in appendix A.
</span></li></ul>
</section>
-<section class="appendix" id="changes-from-candidate-recommendation-to-this-version">
- <h3><span class="secno"><span class="delete">B.1</span><span class="insert">B.2</span> </span>Changes from Candidate Recommendation to this version</h3>
+<section class="appendix" id="changes-from-candidate-recommendation-to-proposed-recommendation">
+ <h3><span class="secno"><span class="delete">B.1</span><span class="insert">B.2</span> </span>Changes from Candidate Recommendation to <span class="delete">this version</span><span class="insert">Proposed Recommendation</span></h3>
<p> Please see the <a href="http://www.w3.org/2011/prov/wiki/ResponsesToPublicCommentsCR">
Responses to Public Comments on the Candidate Recommendation</a>
for more details about the justification of these changes.</p>
--- a/model/releases/REC-prov-dm-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/releases/REC-prov-dm-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -906,7 +906,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
--- a/model/releases/REC-prov-dm-20130430/diff.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/releases/REC-prov-dm-20130430/diff.html Sun Apr 14 19:44:18 2013 +0200
@@ -919,7 +919,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and <span class="delete">Dublic</span><span class="insert">Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
--- a/model/releases/REC-prov-n-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/releases/REC-prov-n-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -882,7 +882,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
--- a/model/releases/REC-prov-n-20130430/diff-n.html Sun Apr 14 19:43:18 2013 +0200
+++ b/model/releases/REC-prov-n-20130430/diff-n.html Sun Apr 14 19:44:18 2013 +0200
@@ -895,7 +895,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> <span class="delete">(To be published as Note), the</span><span class="insert">(Note),</span> mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> provides a mapping between <span class="delete">PROV</span><span class="insert">PROV-O</span> and <span class="delete">Dublic</span><span class="insert">Dublin</span> Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> <span class="delete">(To be published as Note),</span><span class="insert">(Note),</span> a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> <span class="delete">(To be published as Note)</span><span class="insert">(Note)</span> introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
--- a/ontology/ProvenanceOntology.owl Sun Apr 14 19:43:18 2013 +0200
+++ b/ontology/ProvenanceOntology.owl Sun Apr 14 19:44:18 2013 +0200
@@ -28,7 +28,6 @@
<owl:versionIRI rdf:resource="http://www.w3.org/ns/prov-o-20130312"/>
</owl:Ontology>
- <owl:Ontology rdf:about="http://www.w3.org/ns/prov#"></owl:Ontology>
<!--
@@ -88,10 +87,10 @@
<rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
</owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&owl;versionInfo"/>
<owl:AnnotationProperty rdf:about="&rdfs;seeAlso">
<rdfs:comment xml:lang="en"></rdfs:comment>
</owl:AnnotationProperty>
+ <owl:AnnotationProperty rdf:about="&owl;versionInfo"/>
<owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#specializationOf">
<rdfs:label>specializationOf</rdfs:label>
<constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
@@ -849,8 +848,8 @@
</owl:propertyChainAxiom>
</owl:ObjectProperty>
<owl:Axiom>
+ <rdfs:comment>Attribution is a particular case of trace (see http://www.w3.org/TR/prov-dm/#concept-trace), in the sense that it links an entity to the agent that ascribed it.</rdfs:comment>
<definition>IF wasAttributedTo(e2,ag1,aAttr) holds, THEN wasInfluencedBy(e2,ag1) also holds. </definition>
- <rdfs:comment>Attribution is a particular case of trace (see http://www.w3.org/TR/prov-dm/#concept-trace), in the sense that it links an entity to the agent that ascribed it.</rdfs:comment>
<owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
<owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasAttributedTo"/>
<owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
@@ -935,13 +934,13 @@
<owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasInfluencedBy">
<rdfs:label>wasInfluencedBy</rdfs:label>
<rdfs:comment xml:lang="en">Because prov:wasInfluencedBy is a broad relation, its more specific subproperties (e.g. prov:wasInformedBy, prov:actedOnBehalfOf, prov:wasEndedBy, etc.) should be used when applicable.</rdfs:comment>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
<editorialNote xml:lang="en">The sub-properties of prov:wasInfluencedBy can be elaborated in more detail using the Qualification Pattern. For example, the binary relation :baking prov:used :spoon can be qualified by asserting :baking prov:qualifiedUsage [ a prov:Usage; prov:entity :spoon; prov:atLocation :kitchen ] .
Subproperties of prov:wasInfluencedBy may also be asserted directly without being qualified.
prov:wasInfluencedBy should not be used without also using one of its subproperties.
</editorialNote>
+ <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
<category>qualified</category>
<inverse>influenced</inverse>
<component>agents-responsibility</component>
@@ -984,8 +983,8 @@
</owl:annotatedTarget>
</owl:Axiom>
<owl:Axiom>
+ <definition>influencee: an identifier (o2) for an entity, activity, or agent; </definition>
<dm>http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <definition>influencee: an identifier (o2) for an entity, activity, or agent; </definition>
<owl:annotatedProperty rdf:resource="&rdfs;domain"/>
<owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
<owl:annotatedTarget>
@@ -1597,7 +1596,7 @@
<rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Agent"/>
<dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
<n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
- <definition>Agents of type Organization are social institutions such as companies, societies etc.</definition>
+ <definition>An organization is a social or legal institution such as a company, society, etc.</definition>
<category>expanded</category>
<component>agents-responsibility</component>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
@@ -1613,8 +1612,8 @@
<dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
<n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
<category>expanded</category>
- <definition xml:lang="en">Agents of type Person are people.</definition>
<component>agents-responsibility</component>
+ <definition xml:lang="en">Person agents are people.</definition>
<rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
</owl:Class>
--- a/ontology/releases/FR-prov-o/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,10609 +0,0 @@
-<!DOCTYPE html PUBLIC '-//W3C//DTD HTML 4.01 Transitional//EN' 'http://www.w3.org/TR/html4/loose.dtd'>
-<html lang="en" dir="ltr">
-<head>
- <title>PROV-O: The PROV Ontology</title>
- <meta http-equiv="Content-Type" content="text/html;charset=utf-8">
- <link rel="http://www.w3.org/ns/prov#has_provenance" href="http://www.w3.org/2011/prov/provenance/prov-o">
-
- <style type="text/css">
- /* prov:wasQuotedFrom http://speronitomcat.web.cs.unibo.it:8080/LODE/owl.css */
- .RFC2119 {
- text-transform: lowercase;
- font-style: italic;
- }
- .nonterminal {
- font-weight: bold;
- font-family: sans-serif;
- font-size: 95%;
- }
- #abstract br {
- /* doesn't work right SOMETIMES
- margin-bottom: 1em; */
- }
- .name {
- font-family: monospace;
- }
- .buttonpanel {
- margin-top: 1ex;
- margin-bottom: 1ex;
- padding-left: 1ex;
- padding-right: 1ex;
- padding-top: 1ex;
- padding-bottom: 0.6ex;
- border: 1px dotted black;
- }
- .grammar {
- margin-top: 1ex;
- margin-bottom: 1ex;
- padding-left: 1ex;
- padding-right: 1ex;
- padding-top: 1ex;
- padding-bottom: 0.6ex;
- border: 1px dashed #2f6fab;
- font-family: monospace;
- }
- .image {
- text-align: center;
- }
- .centered {
- text-align: center;
- padding-top: 4ex;
- padding-bottom: 4ex;
- }
- .centered table {
- margin: 0 auto;
- text-align: left;
- }
- .caption {
- font-weight: bold;
- }
- .indent {
- margin-left: 20px;
- }
- .atrisknote {
- padding: 5px;
- margin-top: 10px;
- margin-bottom: 10px;
- border: solid 2px blue;
- background-color: #FFA;
- }
- .atrisknotehead {
- font-style: italic;
- }
-
- /* Stying the examples. */
-
- .anexample:before {
- content: "Example:";
- font-family: sans-serif;
- font-size: 1.6ex;
- font-weight: bold;
- }
- .anexample {
- margin-top: 1ex;
- margin-bottom: 1ex;
- padding-left: 1ex;
- padding-right: 1ex;
- padding-top: 1ex;
- padding-bottom: 0.6ex;
- border: 1px dashed #2f6fab;
- background-color: #f9f9f9;
- }
- .anexample table {
- background-color: #f9f9f9;
- }
-
- /* Styling the parts in the functional-style syntax. */
-
- div.fss {
- margin-top: 10px;
- margin-bottom: 10px;
- margin-left: 20px;
- margin-right: 20px;
- font-family: monospace;
- }
- table.fss {
- margin: 0px 0px 0px 0px;
- padding: 0px 0px 0px 0px;
- width: 100%;
- }
- table.fss caption.fss {
- font-size: 1.5ex;
- font-weight: bold;
- text-align: left;
- padding-left: 10px;
- }
- table.fss td:first-child {
- font-family: monospace;
- padding-left: 20px;
- padding-right: 20px;
- width: 60%;
- }
-
- /* Styling the parts in the RDF syntax. */
-
- div.rdf{
- margin-top: 10px;
- margin-bottom: 10px;
- margin-left: 20px;
- margin-right: 20px;
- font-family: monospace;
- }
- table.rdf {
- margin: 0px 0px 0px 0px;
- padding: 0px 0px 0px 0px;
- width: 100%;
- }
- table.rdf caption.rdf {
- font-size: 1.5ex;
- font-weight: bold;
- text-align: left;
- padding-left: 10px;
- }
- table.rdf td:first-child {
- font-family: monospace;
- padding-left: 20px;
- padding-right: 20px;
- width: 60%;
- }
-
- /* Styling the XML syntax. */
-
- div.xmlsyn {
- margin-top: 10px;
- margin-bottom: 10px;
- margin-left: 20px;
- margin-right: 20px;
- font-family: monospace;
- }
- div.axioms {
- margin-top: 10px;
- margin-bottom: 10px;
- margin-left: 20px;
- margin-right: 20px;
- }
-
- /* Other styles. */
-
- table.complexity td {
- text-align: center;
- }
- table.allname td {
- font-family: monospace;
- }
- table.canonicalparsing {
- margin-left: 20px;
- border-style: none;
- }
- table.canonicalparsing td {
- vertical-align: top;
- padding: 2px 2px 2px 2px;
- }
- table.canonicalparsing td.two {
- padding-left: 30px;
- }
-
- /* The following are classes for templates used in the editing process. */
-
- .review {
- padding: 5px;
- border: solid 1px black;
- margin-left: 10%;
- margin-top: 10px;
- margin-bottom: 10px;
- background-color: #FFA;
- font-size: smaller;
- }
- .reviewauthor {
- font-size: smaller;
- font-style: italic;
- }
- .ednote {
- padding: 5px;
- border: solid 1px black;
- margin-top: 10px;
- margin-bottom: 10px;
- }
- .ednotehead {
- font-weight: bold;
- }
-
- /* override mediawiki's beautiful DL styling... */
- dl {
- background: white;
- width: 100%;
- border: none;
- margin-top: 0;
- margin-bottom: 0;
- padding-top: 0;
- padding-bottom: 0;
- }
-
- div {
- margin-top: 0;
- margin-bottom: 0;
- }
- #fulltitle {
- font-size: 140%;
- font-weight: bold;
- }
-
- .xml {
- color: red
- }
-
- .rdbms{
- color: red
- }
-
- /* just copying from wiki, so it stays through TR. Currently
- affects Primer, at least */
- pre {
- background-color:#F9F9F9;
- border:1px dashed #2F6FAB;
- color:black;
- line-height:1.1em;
- padding:1em;
- }
- </style>
-
- <style type="text/css">
- /* prov:wasQuotedFrom http://speronitomcat.web.cs.unibo.it:8080/LODE/Primer.css . */
-
- /* define a class "noprint" for sections which don't get printed */
- .noprint { display: none; }
-
- /* our syntax menu for switching */
- div.syntaxmenu {
- border: 1px dotted black;
- padding:0.5em;
- margin: 1em;
- }
-
- @media print {
- div.syntaxmenu { display:none; }
- }
-
- /* use tab-like headers for syntax examples */
- div.exampleheader {
- font-size: 90%;
- float: left;
- background: #F9F9F9;
- color: #2F6FAB;
- border: 1px dashed #2F6FAB;
- border-bottom: 0px;
- padding-top: 2px;
- }
-
- div.exampleheader span.exampleheader {
- background: #F9F9F9;
- padding-top: 0px;
- padding-right: 10px;
- padding-left: 10px;
- padding-bottom: 3px;
- padding-top: 0px;
- }
-
- /* Also copy MediaWiki style here, so it will not look different when exported */
- div.fssyntax pre, div.rdfxml pre, div.owlxml pre, div.turtle pre, div.manchester pre {
- background-color: #F9F9F9;
- border: 1px dashed #2F6FAB;
- color: black;
- line-height: 1.1em;
- padding: 1em;
- clear: both;
- margin-left: 0em;
- }
- /* (further styles directly embedded in header template) */
- </style>
-
- <style type="text/css">
- /* prov:wasDerivedFrom http://speronitomcat.web.cs.unibo.it:8080/LODE/rec.css . */
-
- /* Style for a "Recommendation" */
-
- /*
- Copyright 1997-2003 W3C (MIT, ERCIM, Keio). All Rights Reserved.
- The following software licensing rules apply:
- http://www.w3.org/Consortium/Legal/copyright-software */
-
- /* $Id: base.css,v 1.25 2006/04/18 08:42:53 bbos Exp $ */
-
- body {
- padding: 2em 1em 2em 70px;
- margin: 0;
- font-family: sans-serif;
- color: black;
- background: white;
- background-position: top left;
- background-attachment: fixed;
- background-repeat: no-repeat;
- }
- :link { color: #00C; background: transparent }
- :visited { color: #609; background: transparent }
- a:active { color: #C00; background: transparent }
-
- a:link img, a:visited img { border-style: none } /* no border on img links */
-
- a img { color: white; } /* trick to hide the border in Netscape 4 */
- @media all { /* hide the next rule from Netscape 4 */
- a img { color: inherit; } /* undo the color change above */
- }
-
- th, td { /* ns 4 */
- font-family: sans-serif;
- }
-
- h1, h2, h3, h4, h5, h6 { text-align: left }
- /* background should be transparent, but WebTV has a bug */
- h1, h2, h3 { color: #005A9C; background: white }
- h1 { font: 170% sans-serif }
- h2 { font: 140% sans-serif }
- h3 { font: 120% sans-serif }
- h4 { font: bold 100% sans-serif }
- h5 { font: italic 100% sans-serif }
- h6 { font: small-caps 100% sans-serif }
-
- .hide { display: none }
-
- div.head { margin-bottom: 1em }
- div.head h1 { margin-top: 2em; clear: both }
- div.head table { margin-left: 2em; margin-top: 2em }
-
- p.copyright { font-size: small }
- p.copyright small { font-size: small }
-
- @media screen { /* hide from IE3 */
- a[href]:hover { background: #ffa }
- }
-
- pre { margin-left: 2em }
- /*
- p {
- margin-top: 0.6em;
- margin-bottom: 0.6em;
- }
- */
- dt, dd { margin-top: 0; margin-bottom: 0 } /* opera 3.50 */
- dt { font-weight: bold }
-
- pre, code { font-family: monospace } /* navigator 4 requires this */
-
- ul.toc, ol.toc {
- list-style: disc; /* Mac NS has problem with 'none' */
- list-style: none;
- }
-
- /*@media aural {
- h1, h2, h3 { stress: 20; richness: 90 }
- .hide { speak: none }
- p.copyright { volume: x-soft; speech-rate: x-fast }
- dt { pause-before: 20% }
- pre { speak-punctuation: code }
- }*/
-
- /*body {
- background-image: url(http://lode.sourceforge.net/img/LODELogo.png);
- }*/
- </style>
-
- <style type="text/css">
- /* prov:wasQuotedFrom http://speronitomcat.web.cs.unibo.it:8080/LODE/extra.css . */
-
- body {
- text-align: justify;
- }
-
- h1 {
- line-height: 110%;
- }
-
- .hlist {
- border: 1px solid navy;
- padding:5px;
- background-color: #F4FFFF;
- }
-
- .hlist li {
- display: inline;
- display: inline-table;
- list-style-type: none;
- padding-right: 20px;
-
- }
-
- .entity {
- border: 1px solid navy;
- margin:5px 0px 5px 0px;
- padding: 5px;
- }
-
- .type-c {
- cursor:help;
- color:orange;
- }
-
- .type-op {
- cursor:help;
- color:navy;
- }
-
- .type-dp {
- cursor:help;
- color:green;
- }
-
- .type-ap {
- cursor:help;
- color:maroon;
- }
-
- .type-ni {
- cursor:help;
- color:brown;
- }
-
- .logic {
- color:purple;
- font-weight:bold;
- }
-
- h3 {
- margin-top: 3px;
- padding-bottom: 5px;
- border-bottom: 1px solid navy;
- }
-
- h2 {
- margin-top:40px;
- }
-
- .dotted {
- border-bottom: 1px dotted gray;
- }
-
- dt {
- margin-top:5px;
- }
-
- .description {
- border-top: 1px dashed gray;
- border-bottom: 1px dashed gray;
- background-color: rgb(242, 243, 244);
- margin-top:5px;
- padding-bottom:5px;
- }
-
- .description dl {
- background-color: rgb(242, 243, 244);
- }
-
- .description ul {
- padding-left: 12px;
- margin-top: 0px;
- }
-
- .backlink {
- font-size:10pt;
- text-align:right;
- float:right;
- color:black;
- padding: 2px;
- border: 1px dotted navy;
- background-color: #F4FFFF;
- }
-
- .imageblock {
- text-align: center;
- }
-
- .imageblock img {
- border:1px solid gray;
- }
-
- .endnote {
- margin-top: 40px;
- border-top: 1px solid gray;
- padding-top: 10px;
- text-align: center;
- color:gray;
- font-size:50%;
- }
- </style>
- <!-- link rel="provenance" href="http://www.w3.org/2007/08/pyRdfa/extract?format=turtle&uri=http://aquarius.tw.rpi.edu/prov-wg/prov-o"/ -->
-
- <!--
- === NOTA BENE ===
- For the three scripts below, if your spec resides on dev.w3 you can check them
- out in the same tree and use relative links so that they'll work offline,
- -->
-
- <!-- From DM -->
-
- <!-- From DM -->
- <style type="text/css">
- .note { font-size:small; margin-left:50px }
- table { text-align: center; vertical-align: middle }
-
- table.thinborder {
- border-width: 1px;
- border-spacing: 0px;
- border-style: none;
- border-color: gray;
- border-collapse: collapse;
- }
- table.thinborder th {
- border-width: 1px;
- padding: 0px;
- border-style: solid;
- border-color: gray;
- }
- table.thinborder td {
- border-width: 1px;
- padding: 2px;
- border-style: solid;
- border-color: gray;
- background-color: rgb(246,246,246);
- }
- </style>
-
- <style type="text/css">
- /* This CSS written by Tim Lebo for PROV-O HTML (all other CSS was taken from elsewhere) */
- table.qualified-forms {
- width: 75%;
- }
- ul.hlist {
- margin: 20px;
- }
- table {
- margin: 20px;
- border:1px solid navy;
- background-color: #F4FFFF;
- }
- table th {
- background-color: LightGoldenRodYellow;
- }
- table tr {
- padding: 2px;
- border: 1px solid navy;
- }
- table td {
- text-align: left;
- padding-top: 5px;
- padding-bottom: 5px;
- padding-left: 15px;
- padding-right: 15px;
- }
- table td.prov-attribute {
- width: 20%
- }
- table.prov-detail a:visited {
- color:black; text-decoration:none;
- }
- table.prov-detail a:link {
- color:black; text-decoration:none;
- }
- .component-entities-activities {
- border:1px solid gray;
- background-color: #FFD4D4
- }
- .component-agents-responsibility {
- border:1px solid gray;
- background-color: #CCD9EE;
- }
- .component-derivations {
- border:1px solid gray;
- background-color: #CCEED9;
- }
- .component-collections {
- border:1px solid gray;
- background-color: #CED4D4;
- }
- .component-alternate {
- border:1px solid gray;
- background-color: #F4FFD9;
- }
- .component-annotations {
- border:1px solid gray;
- background-color: #FCE1CE;
- }
- span.repeated {
- font-family: monospace;
- }
- a.qname {
- font-family: monospace;
- }
- strong.crossreference {
- padding-right: 15px;
- }
- div.feature-at-risk {
- color: red;
- }
- </style>
-
-
-
-
-
- <style type="text/css">
-/*****************************************************************
- * ReSpec CSS
- * Robin Berjon (robin at berjon dot com)
- * v0.05 - 2009-07-31
- *****************************************************************/
-
-
-/* --- INLINES --- */
-em.rfc2119 {
- text-transform: lowercase;
- font-variant: small-caps;
- font-style: normal;
- color: #900;
-}
-
-h1 acronym, h2 acronym, h3 acronym, h4 acronym, h5 acronym, h6 acronym, a acronym,
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- border: none;
-}
-
-dfn {
- font-weight: bold;
-}
-
-a.internalDFN {
- color: inherit;
- border-bottom: 1px solid #99c;
- text-decoration: none;
-}
-
-a.externalDFN {
- color: inherit;
- border-bottom: 1px dotted #ccc;
- text-decoration: none;
-}
-
-a.bibref {
- text-decoration: none;
-}
-
-code {
- color: #ff4500;
-}
-
-
-/* --- WEB IDL --- */
-pre.idl {
- border-top: 1px solid #90b8de;
- border-bottom: 1px solid #90b8de;
- padding: 1em;
- line-height: 120%;
-}
-
-pre.idl::before {
- content: "WebIDL";
- display: block;
- width: 150px;
- background: #90b8de;
- color: #fff;
- font-family: initial;
- padding: 3px;
- font-weight: bold;
- margin: -1em 0 1em -1em;
-}
-
-.idlType {
- color: #ff4500;
- font-weight: bold;
- text-decoration: none;
-}
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-/*.idlModule*/
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-.idlInterfaceID, .idlDictionaryID {
- font-weight: bold;
- color: #005a9c;
-}
-
-.idlSuperclass {
- font-style: italic;
- color: #005a9c;
-}
-
-/*.idlAttribute*/
-.idlAttrType, .idlFieldType, .idlMemberType {
- color: #005a9c;
-}
-.idlAttrName, .idlFieldName, .idlMemberName {
- color: #ff4500;
-}
-.idlAttrName a, .idlFieldName a, .idlMemberName a {
- color: #ff4500;
- border-bottom: 1px dotted #ff4500;
- text-decoration: none;
-}
-
-/*.idlMethod*/
-.idlMethType {
- color: #005a9c;
-}
-.idlMethName {
- color: #ff4500;
-}
-.idlMethName a {
- color: #ff4500;
- border-bottom: 1px dotted #ff4500;
- text-decoration: none;
-}
-
-/*.idlParam*/
-.idlParamType {
- color: #005a9c;
-}
-.idlParamName {
- font-style: italic;
-}
-
-.extAttr {
- color: #666;
-}
-
-/*.idlConst*/
-.idlConstType {
- color: #005a9c;
-}
-.idlConstName {
- color: #ff4500;
-}
-.idlConstName a {
- color: #ff4500;
- border-bottom: 1px dotted #ff4500;
- text-decoration: none;
-}
-
-/*.idlException*/
-.idlExceptionID {
- font-weight: bold;
- color: #c00;
-}
-
-.idlTypedefID, .idlTypedefType {
- color: #005a9c;
-}
-
-.idlRaises, .idlRaises a.idlType, .idlRaises a.idlType code, .excName a, .excName a code {
- color: #c00;
- font-weight: normal;
-}
-
-.excName a {
- font-family: monospace;
-}
-
-.idlRaises a.idlType, .excName a.idlType {
- border-bottom: 1px dotted #c00;
-}
-
-.excGetSetTrue, .excGetSetFalse, .prmNullTrue, .prmNullFalse, .prmOptTrue, .prmOptFalse {
- width: 45px;
- text-align: center;
-}
-.excGetSetTrue, .prmNullTrue, .prmOptTrue { color: #0c0; }
-.excGetSetFalse, .prmNullFalse, .prmOptFalse { color: #c00; }
-
-.idlImplements a {
- font-weight: bold;
-}
-
-dl.attributes, dl.methods, dl.constants, dl.fields, dl.dictionary-members {
- margin-left: 2em;
-}
-
-.attributes dt, .methods dt, .constants dt, .fields dt, .dictionary-members dt {
- font-weight: normal;
-}
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-.methods dt code {
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- border-collapse: collapse;
- margin: 0.5em 0;
- width: 100%;
-}
-table.parameters { border-bottom: 1px solid #90b8de; }
-table.exceptions { border-bottom: 1px solid #deb890; }
-
-.parameters th, .exceptions th {
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- padding: 3px 5px;
- text-align: left;
- font-family: initial;
- font-weight: normal;
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-}
-.parameters th { background: #90b8de; }
-.exceptions th { background: #deb890; }
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-.parameters td, .exceptions td {
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-.parameters tr:first-child td, .exceptions tr:first-child td {
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-/* --- TOC --- */
-.toc a {
- text-decoration: none;
-}
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-a .secno {
- color: #000;
-}
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-/* --- TABLE --- */
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-.simple th {
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-.simple th[scope="row"] {
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-.simple td {
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-.simple tr:nth-child(even) {
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-}
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-/* --- DL --- */
-.section dd > p:first-child {
- margin-top: 0;
-}
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-.section dd > p:last-child {
- margin-bottom: 0;
-}
-
-.section dd {
- margin-bottom: 1em;
-}
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-.section dl.attrs dd, .section dl.eldef dd {
- margin-bottom: 0;
-}
-
-/* --- EXAMPLES --- */
-pre.example {
- border-top: 1px solid #ff4500;
- border-bottom: 1px solid #ff4500;
- padding: 1em;
- margin-top: 1em;
-}
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-pre.example::before {
- content: "Example";
- display: block;
- width: 150px;
- background: #ff4500;
- color: #fff;
- font-family: initial;
- padding: 3px;
- font-weight: bold;
- margin: -1em 0 1em -1em;
-}
-
-/* --- EDITORIAL NOTES --- */
-.issue {
- padding: 1em;
- margin: 1em 0em 0em;
- border: 1px solid #f00;
- background: #ffc;
-}
-
-.issue::before {
- content: "Issue";
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- width: 150px;
- margin: -1.5em 0 0.5em 0;
- font-weight: bold;
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-.note {
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- display: block;
- width: 150px;
- margin: -1.5em 0 0.5em 0;
- font-weight: bold;
- border: 1px solid #cff6d9;
- background: #fff;
- padding: 3px 1em;
-}
-
-/* --- Best Practices --- */
-div.practice {
- border: solid #bebebe 1px;
- margin: 2em 1em 1em 2em;
-}
-
-span.practicelab {
- margin: 1.5em 0.5em 1em 1em;
- font-weight: bold;
- font-style: italic;
-}
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-span.practicelab { background: #dfffff; }
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- top: -1.5em;
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-p.practicedesc {
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- position: relative;
- top: -2em;
- padding: 0;
- margin: 1.5em 0.5em -1em 1em;
- }
-}
-
-/* --- SYNTAX HIGHLIGHTING --- */
-pre.sh_sourceCode {
- background-color: white;
- color: black;
- font-style: normal;
- font-weight: normal;
-}
-
-pre.sh_sourceCode .sh_keyword { color: #005a9c; font-weight: bold; } /* language keywords */
-pre.sh_sourceCode .sh_type { color: #666; } /* basic types */
-pre.sh_sourceCode .sh_usertype { color: teal; } /* user defined types */
-pre.sh_sourceCode .sh_string { color: red; font-family: monospace; } /* strings and chars */
-pre.sh_sourceCode .sh_regexp { color: orange; font-family: monospace; } /* regular expressions */
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-<link href="http://www.w3.org/StyleSheets/TR/W3C-REC" rel="stylesheet" type="text/css" charset="utf-8"></head>
- <body style="display: inherit;"><div class="head"><p><a href="http://www.w3.org/"><img width="72" height="48" src="http://www.w3.org/Icons/w3c_home" alt="W3C"></a></p><h1 class="title" id="title">PROV-O: The PROV Ontology</h1><h2 id="w3c-recommendation-30-april-2013"><acronym title="World Wide Web Consortium">W3C</acronym> Recommendation 30 April 2013</h2><dl><dt>This version:</dt><dd><a href="http://www.w3.org/TR/2013/REC-prov-o-20130430/">http://www.w3.org/TR/2013/REC-prov-o-20130430/</a></dd><dt>Latest published version:</dt><dd><a href="http://www.w3.org/TR/prov-o/">http://www.w3.org/TR/prov-o/</a></dd><dt>Implementation report:</dt><dd><a href="http://www.w3.org/TR/2013/NOTE-prov-implementations-20130430/">http://www.w3.org/TR/2013/NOTE-prov-implementations-20130430/</a></dd><dt>Previous version:</dt><dd><a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">http://www.w3.org/TR/2013/PR-prov-o-20130312/</a></dd>
-
-<dt>Editors:</dt><dd><a href="http://tw.rpi.edu/instances/TimLebo">Timothy Lebo</a>, Rensselaer Polytechnic Institute, USA</dd>
-<dd><a href="http://cci.case.edu/cci/index.php/Satya_Sahoo">Satya Sahoo</a>, Case Western Reserve University, USA</dd>
-<dd><a href="http://tw.rpi.edu/instances/Deborah_L_McGuinness">Deborah McGuinness</a>, Rensselaer Polytechnic Institute, USA</dd>
-<dt>Contributors:</dt><dd><span>(In alphabetical order)</span></dd>
-<dd><a href="http://semanticweb.org/wiki/Khalid_Belhajjame">Khalid Belhajjame</a>, University of Manchester, UK</dd>
-<dd><a href="http://homepages.inf.ed.ac.uk/jcheney/">James Cheney</a>, University of Edinburgh, UK</dd>
-<dd><a href="http://homepages.abdn.ac.uk/dcorsar/pages/">David Corsar</a>, University of Aberdeen, UK</dd>
-<dd><a href="http://www.oeg-upm.net/index.php/en/phdstudents/28-dgarijo">Daniel Garijo</a>, Universidad Politécnica de Madrid, Spain</dd>
-<dd><a href="http://soiland-reyes.com/stian/">Stian Soiland-Reyes</a>, University of Manchester, UK</dd>
-<dd><a href="http://tw.rpi.edu/web/person/StephanZednik">Stephan Zednik</a>, Rensselaer Polytechnic Institute, USA</dd>
-<dd><a href="http://users.ox.ac.uk/~zool0770/">Jun Zhao</a>, University of Oxford, UK</dd>
-</dl>
-
- <p>
- Please refer to the <a href="http://www.w3.org/2011/prov/errata.html"><strong>errata</strong></a> for this document, which may include some normative corrections.
- </p>
-
-<p>The English version of this specification is the only normative version. Non-normative <a href="http://www.w3.org/Consortium/Translation/">translations</a> may also be available.</p>
-
-<p class="copyright"><a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> © 2011-2013 <a href="http://www.w3.org/"><acronym title="World Wide Web Consortium">W3C</acronym></a><sup>®</sup> (<a href="http://www.csail.mit.edu/"><acronym title="Massachusetts Institute of Technology">MIT</acronym></a>, <a href="http://www.ercim.eu/"><acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym></a>, <a href="http://www.keio.ac.jp/">Keio</a>, <a href="http://ev.buaa.edu.cn/">Beihang</a>), All Rights Reserved. W3C <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> rules apply.</p>
-
-
-<hr></div>
-
- <div id="abstract" class="introductory section"><h2>Abstract</h2>
- <p>The PROV Ontology (PROV-O) expresses the PROV Data Model [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>] using the OWL2 Web Ontology Language (OWL2) [<cite><a class="bibref" rel="biblioentry" href="#bib-OWL2-OVERVIEW">OWL2-OVERVIEW</a></cite>]. It provides a set of classes, properties, and restrictions that can be used to represent and interchange provenance information generated in different systems and under different contexts.
-It can also be specialized to create new classes and properties to model provenance information for different applications and domains.
- The <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/">PROV Document Overview</a> describes the overall state of PROV, and should be read before other PROV documents.
- </p>
-
-
- <p style="text-align: center;">The namespace for all PROV-O terms is <span class="repeated">http://www.w3.org/ns/prov#</span>.
- </p>
-
- <p style="text-align: center;">The OWL encoding of the PROV Ontology is available <a href="http://www.w3.org/ns/prov-o">here</a>.
- </p>
- </div>
-
-
-
-
-<div id="sotd" class="introductory section">
-<h2>Status of This Document</h2>
-
-
-
- <p>
- <em>This section describes the status of this document at the time of its publication. Other
- documents may supersede this document. A list of current <abbr title="World Wide Web Consortium">W3C</abbr> publications and the latest revision
- of this technical report can be found in the <a href="http://www.w3.org/TR/"><abbr title="World Wide Web Consortium">W3C</abbr> technical reports
- index</a> at http://www.w3.org/TR/.</em>
- </p>
-
-<h4 id="prov-family-of-documents">PROV Family of Documents</h4>
-This document is part of the PROV family of documents, a set of documents defining various aspects that are necessary to achieve the vision of inter-operable
-interchange of provenance information in heterogeneous environments such as the Web. These documents are listed below. Please consult the [<cite><a class="bibref" href="#bib-PROV-OVERVIEW">PROV-OVERVIEW</a></cite>] for a guide to reading these documents.
-<ul>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-overview-20130430/">PROV-OVERVIEW</a> (Note), an overview of the PROV family of documents [<cite><a class="bibref" href="#bib-PROV-OVERVIEW">PROV-OVERVIEW</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-primer-20130430/">PROV-PRIMER</a> (Note), a primer for the PROV data model [<cite><a class="bibref" href="#bib-PROV-PRIMER">PROV-PRIMER</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/REC-prov-o-20130430/">PROV-O</a> (Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of the PROV data model to RDF (this document);</li>
-<li> <a href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/">PROV-DM</a> (Recommendation), the PROV data model for provenance [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/REC-prov-n-20130430/">PROV-N</a> (Recommendation), a notation for provenance aimed at human consumption [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/">PROV-CONSTRAINTS</a> (Recommendation), a set of constraints applying to the PROV data model [<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
-</ul>
-
-<h4 id="endorsed-by-w3c">Endorsed By <abbr title="World Wide Web Consortium">W3C</abbr></h4>
-
-<p>This document has been reviewed by <abbr title="World Wide Web Consortium">W3C</abbr> Members, by software developers, and by other <abbr title="World Wide Web Consortium">W3C</abbr> groups and interested parties, and is endorsed by the Director as a <abbr title="World Wide Web Consortium">W3C</abbr> Recommendation. It is a stable document and may be used as reference material or cited from another document. <abbr title="World Wide Web Consortium">W3C</abbr>'s role in making the Recommendation is to draw attention to the specification and to promote its widespread deployment. This enhances the functionality and interoperability of the Web.</p>
-
-<h4 id="please-send-comments">Please Send Comments</h4>
-
- <p>
- This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as a Recommendation.
-
-
- If you wish to make comments regarding this document, please send them to
- <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a>
- (<a href="mailto:public-prov-comments-request@w3.org?subject=subscribe">subscribe</a>,
- <a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archives</a>).
-
-
-
-
- All comments are welcome.
-
-
-
- </p><p>
-
- This document was produced by a group operating under the
- <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February 2004 <abbr title="World Wide Web Consortium">W3C</abbr> Patent Policy</a>.
-
-
-
-
- <abbr title="World Wide Web Consortium">W3C</abbr> maintains a <a href="http://www.w3.org/2004/01/pp-impl/46974/status" rel="disclosure">public list of any patent disclosures</a>
-
- made in connection with the deliverables of the group; that page also includes instructions for
- disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains
- <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential Claim(s)</a> must disclose the
- information in accordance with <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section
- 6 of the <abbr title="World Wide Web Consortium">W3C</abbr> Patent Policy</a>.
-
-
- </p>
-
-
-
-
-</div>
-
-
-
-
-
-<div id="toc" class="section"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1. </span>Introduction</a><ul class="toc"><li class="tocline"><a href="#compliance" class="tocxref"><span class="secno">1.1 </span>Compliance with this Document</a></li><li class="tocline"><a href="#notations" class="tocxref"><span class="secno">1.2 </span>Notational Conventions</a></li><li class="tocline"><a href="#namespaces" class="tocxref"><span class="secno">1.3 </span>Namespaces</a></li></ul></li><li class="tocline"><a href="#prov-o-at-a-glance" class="tocxref"><span class="secno">2. </span>PROV-O at a glance</a></li><li class="tocline"><a href="#description" class="tocxref"><span class="secno">3. </span>The PROV-O Ontology Description</a><ul class="toc"><li class="tocline"><a href="#description-starting-point-terms" class="tocxref"><span class="secno">3.1 </span>Starting Point Terms</a></li><li class="tocline"><a href="#description-expanded-terms" class="tocxref"><span class="secno">3.2 </span>Expanded Terms</a></li><li class="tocline"><a href="#description-qualified-terms" class="tocxref"><span class="secno">3.3 </span>Qualified Terms</a></li></ul></li><li class="tocline"><a href="#cross-reference" class="tocxref"><span class="secno">4. </span>Cross reference for PROV-O classes and properties</a><ul class="toc"><li class="tocline"><a href="#cross-reference-starting-point-terms" class="tocxref"><span class="secno">4.1 </span>Starting Point Terms</a></li><li class="tocline"><a href="#cross-reference-expanded-terms" class="tocxref"><span class="secno">4.2 </span>Expanded Terms</a></li><li class="tocline"><a href="#cross-reference-qualified-terms" class="tocxref"><span class="secno">4.3 </span>Qualified Terms</a></li><li class="tocline"><a href="#cross-reference-index" class="tocxref"><span class="secno">4.4 </span>Term Index</a></li></ul></li><li class="tocline"><a href="#owl-profile" class="tocxref"><span class="secno">A. </span>PROV-O OWL Profile</a></li><li class="tocline"><a href="#inverse-names" class="tocxref"><span class="secno">B. </span>Names of inverse properties</a></li><li class="tocline"><a href="#changes-since-wd-prov-o-20120724" class="tocxref"><span class="secno">C. </span>Changes since WD-prov-o-20120724</a></li>
-
-<li class="tocline"><a href="#changes-since-cr-prov-o-20121211" class="tocxref"><span class="secno">D. </span>Changes since CR-prov-o-20121211</a></li>
-<li class="tocline"><a href="#changes-since-pr-prov-o-20130312" class="tocxref"><span class="secno">E. </span>Changes since PR-prov-o-20130312</a></li>
-
-<li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">F. </span>Acknowledgements</a></li>
-<li class="tocline"><a href="#references" class="tocxref"><span class="secno">G. </span>References</a><ul class="toc">
-<li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">G.1 </span>Normative references</a></li>
-<li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">G.2 </span>Informative references</a></li>
-</ul></li></ul></div>
-
-
-
-
-
- <div id="introduction" class="section">
- <!--OddPage--><h2><span class="secno">1. </span>Introduction</h2>
- <p>The PROV Ontology (PROV-O) defines the OWL2 Web Ontology Language encoding of the PROV Data Model [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>]. This document describes the set of classes, properties, and restrictions that constitute the PROV Ontology. This ontology specification provides the foundation to implement provenance applications in different domains that can represent, exchange, and integrate provenance information generated in different systems and under different contexts. Together with the PROV Access and Query [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-AQ">PROV-AQ</a></cite>] and PROV Data Model [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>], this document forms a framework for provenance information interchange in domain-specific Web-based applications.
- </p>
- <p>
- PROV-O is a lightweight ontology that can be adopted in a wide range of applications.
- With the exception of <a href="#owl-profile">five axioms</a>, PROV-O conforms to the OWL-RL profile [<cite><a class="bibref" rel="biblioentry" href="#bib-OWL2-PRIMER">OWL2-PRIMER</a></cite>].
- The PROV Ontology classes and properties are defined such that they can not only be used directly to represent provenance information,
- but also can be specialized for modeling application-specific provenance details in a variety of domains.
- Thus, the PROV Ontology is expected to be both directly usable in applications as well as serve as a <i>reference model</i>
- for creating domain-specific provenance ontologies and thereby facilitates interoperable provenance modeling.
- To demonstrate the use of PROV-O classes and properties, this document uses an example provenance scenario similar to the one introduced in the PROV-Primer [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-PRIMER">PROV-PRIMER</a></cite>].
- </p>
- <p> The PROV Data Model [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>] introduces a set of concepts to represent provenance information in a variety of application domains. This document maps the PROV Data Model to PROV Ontology using the OWL2 ontology language [<cite><a class="bibref" rel="biblioentry" href="#bib-OWL2-OVERVIEW">OWL2-OVERVIEW</a></cite>].
- </p>
-
- <p> We briefly introduce some of the OWL2 modeling terms that will be used to describe the PROV Ontology.
- An OWL2 <i>instance</i> is an individual object in a domain of discourse, for example a person named Alice or a car named KITT.
- A set of individuals sharing common characteristics constitutes a <i>class</i>.
-
- Person and Car are examples of classes representing the set of individual persons and cars respectively.
- The OWL2 object properties are used to link individuals, classes, or create a property hierarchy.
- For example, the object property "hasOwner" can be used to link car with person.
- The OWL2 datatype properties are used to link individuals or classes to data values, including XML Schema datatypes [<cite><a class="bibref" rel="biblioentry" href="#bib-XMLSCHEMA11-2">XMLSCHEMA11-2</a></cite>].
- </p>
-
- <div id="compliance" class="section">
- <h3><span class="secno">1.1 </span>Compliance with this Document</h3>
- <p>For the purpose of compliance, the normative sections of this document are
- <a href="#compliance">Section 1.1</a>,
- <a href="#notations">Section 1.2</a>,
- <a href="#description">Section 3</a>,
- <a href="#cross-reference">Section 4</a>, and
- <a href="#inverse-names">Appendix B</a>
- </p>
- <ul>
- <li>Information in tables is normative if it appears in a normative section.</li>
- <li>All figures and diagrams are informative.</li>
- <li>All examples are informative.</li>
- </ul>
- </div>
-
- <div id="notations" class="section">
- <h3><span class="secno">1.2 </span>Notational Conventions</h3>
-
- <p>The key words "<em class="rfc2119" title="must">must</em>", "<em class="rfc2119" title="must not">must not</em>", "<em class="rfc2119" title="required">required</em>", "<em class="rfc2119" title="shall">shall</em>", "<em class="rfc2119" title="shall not">shall not</em>", "<em class="rfc2119" title="should">should</em>", "<em class="rfc2119" title="should not">should not</em>", "<em class="rfc2119" title="recommended">recommended</em>", "<em class="rfc2119" title="may">may</em>", and "<em class="rfc2119" title="optional">optional</em>" in this document are to be interpreted as described in [<cite><a class="bibref" rel="biblioentry" href="#bib-RFC2119">RFC2119</a></cite>].</p>
- </div>
-
- <div class="informative section" id="namespaces">
- <h3><span class="secno">1.3 </span>Namespaces</h3><p><em>This section is non-normative.</em></p>
- <p>The following namespace prefixes are used throughout this document.
-
- </p><div style="text-align: left;">
- <table class="thinborder" style="margin-left: auto; margin-right: auto;">
- <caption id="namespace-table"><a href="#namespace-table">Table 1</a>: Prefix and Namespaces used in this specification</caption> <!-- Table 1-->
- <tbody><tr><td><a><b>prefix</b></a></td><td><b>namespace IRI</b></td> <td><b>definition</b></td></tr>
-
- <tr><td><a>rdf</a></td><td>http://www.w3.org/1999/02/22-rdf-syntax-ns#</td><td>The RDF namespace [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-CONCEPTS">RDF-CONCEPTS</a></cite>]</td></tr>
-
- <tr><td><a>xsd</a></td><td>http://www.w3.org/2000/10/XMLSchema#</td><td>XML Schema Namespace [<cite><a class="bibref" rel="biblioentry" href="#bib-XMLSCHEMA11-2">XMLSCHEMA11-2</a></cite>]</td></tr>
-
- <tr><td><a>owl</a></td><td>http://www.w3.org/2002/07/owl#</td><td>The OWL namespace [<cite><a class="bibref" rel="biblioentry" href="#bib-OWL2-OVERVIEW">OWL2-OVERVIEW</a></cite>]</td></tr>
-
- <tr><td><a>prov</a></td><td>http://www.w3.org/ns/prov#</td>
- <td>The PROV namespace [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>]</td></tr>
-
- <tr><td><a>(others)</a></td><td>(various)</td><td>All other namespace prefixes are used in examples only. <br>
- In particular, IRIs starting with "http://example.com" represent<br> some application-dependent IRI [<cite><a class="bibref" rel="biblioentry" href="#bib-IRI">IRI</a></cite>]</td></tr>
- </tbody></table>
- </div>
- </div>
- </div>
-
- <div id="prov-o-at-a-glance" class="informative section">
- <!--OddPage--><h2><span class="secno">2. </span>PROV-O at a glance</h2><p><em>This section is non-normative.</em></p>
-
- <p>PROV-O users may only need to use parts of the entire ontology, depending on their needs and according to how much detail they want to include in their provenance information. For this, the PROV-O terms (classes and properties) are grouped into three categories to provide an incremental introduction to the ontology: Starting Point terms, Expanded terms, and terms for Qualifying relationships.
- </p>
-
- <div id="prov-starting-point-owl-terms-at-a-glance">
- <p><strong>Starting Point classes and properties</strong> provide the basis for the rest of the PROV Ontology and thus it is recommended that readers become comfortable with how to apply these terms before continuing to the remaining categories. These terms are used to create simple provenance descriptions that can be elaborated using terms from other categories. The classes and properties in this category are listed below and are discussed in <a href="#description-starting-point-terms">Section 3.1</a>.</p>
-
-<div class="prov-starting-point owl-classes at-a-glance">
- <ul class="hlist">
- <li>
- <a href="#Entity">prov:Entity</a>
- </li>
- <li>
- <a href="#Activity">prov:Activity</a>
- </li>
- <li>
- <a href="#Agent">prov:Agent</a>
- </li>
- </ul>
-</div>
-
-<div class="prov-starting-point owl-properties at-a-glance">
- <ul class="hlist">
- <li class="object-property">
- <a href="#wasGeneratedBy">prov:wasGeneratedBy</a>
- </li>
- <li class="object-property">
- <a href="#wasDerivedFrom">prov:wasDerivedFrom</a>
- </li>
- <li class="object-property">
- <a href="#wasAttributedTo">prov:wasAttributedTo</a>
- </li>
- <li class="datatype-property">
- <a href="#startedAtTime">prov:startedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#used">prov:used</a>
- </li>
- <li class="object-property">
- <a href="#wasInformedBy">prov:wasInformedBy</a>
- </li>
- <li class="datatype-property">
- <a href="#endedAtTime">prov:endedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#wasAssociatedWith">prov:wasAssociatedWith</a>
- </li>
- <li class="object-property">
- <a href="#actedOnBehalfOf">prov:actedOnBehalfOf</a>
- </li>
- </ul>
-</div>
-
- </div>
-
- <div id="prov-expanded-owl-terms-at-a-glance">
- <p><strong>Expanded classes and properties</strong> provide additional terms that can be used to relate classes in the Starting Point category. The terms in this category are applied in the same way as the terms in the Starting Point category. Many of the terms in this category are subclasses or subproperties of those in the Starting Point category. The classes and properties in this category are listed below and are discussed in <a href="#description-expanded-terms">Section 3.2</a>.</p>
-
-<div class="prov-expanded owl-classes at-a-glance">
- <ul class="hlist">
- <li>
- <a href="#Collection">prov:Collection</a>
- </li>
- <li>
- <a href="#EmptyCollection">prov:EmptyCollection</a>
- </li>
- <li>
- <a href="#Bundle">prov:Bundle</a>
- </li>
- <li>
- <a href="#Person">prov:Person</a>
- </li>
- <li>
- <a href="#SoftwareAgent">prov:SoftwareAgent</a>
- </li>
- <li>
- <a href="#Organization">prov:Organization</a>
- </li>
- <li>
- <a href="#Location">prov:Location</a>
- </li>
- </ul>
-</div>
-
-<div class="prov-expanded owl-properties at-a-glance">
- <ul class="hlist">
- <li class="object-property">
- <a href="#alternateOf">prov:alternateOf</a>
- </li>
- <li class="object-property">
- <a href="#specializationOf">prov:specializationOf</a>
- </li>
- <li class="datatype-property">
- <a href="#generatedAtTime">prov:generatedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#hadPrimarySource">prov:hadPrimarySource</a>
- </li>
- <li class="datatype-property">
- <a href="#value">prov:value</a>
- </li>
- <li class="object-property">
- <a href="#wasQuotedFrom">prov:wasQuotedFrom</a>
- </li>
- <li class="object-property">
- <a href="#wasRevisionOf">prov:wasRevisionOf</a>
- </li>
- <li class="datatype-property">
- <a href="#invalidatedAtTime">prov:invalidatedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#wasInvalidatedBy">prov:wasInvalidatedBy</a>
- </li>
- <li class="object-property">
- <a href="#hadMember">prov:hadMember</a>
- </li>
- <li class="object-property">
- <a href="#wasStartedBy">prov:wasStartedBy</a>
- </li>
- <li class="object-property">
- <a href="#wasEndedBy">prov:wasEndedBy</a>
- </li>
- <li class="object-property">
- <a href="#invalidated">prov:invalidated</a>
- </li>
- <li class="object-property">
- <a href="#influenced">prov:influenced</a>
- </li>
- <li class="object-property">
- <a href="#atLocation">prov:atLocation</a>
- </li>
- <li class="object-property">
- <a href="#generated">prov:generated</a>
- </li>
- </ul>
-</div>
-
- </div>
-
- <div id="prov-qualified-owl-terms-at-a-glance">
- <p><strong>Qualified classes and properties</strong> provide elaborated information about binary relations asserted using Starting Point and Expanded properties. The terms in this category are applied using a pattern that differs from those in the Starting Point and Expanded categories. While the relations from the previous two categories are applied as direct, binary assertions, the terms in this category are used to provide additional attributes of the binary relations. The pattern used in this category allows users to provide elaborate details that are not available using only Starting Point and Expanded terms. The classes and properties in this category are listed below and are discussed in <a href="#description-qualified-terms">Section 3.3</a>.</p>
-
-<div class="prov-qualified owl-classes at-a-glance">
- <ul class="hlist">
- <li>
- <a href="#Influence">prov:Influence</a>
- </li>
- <li>
- <a href="#EntityInfluence">prov:EntityInfluence</a>
- </li>
- <li>
- <a href="#Usage">prov:Usage</a>
- </li>
- <li>
- <a href="#Start">prov:Start</a>
- </li>
- <li>
- <a href="#End">prov:End</a>
- </li>
- <li>
- <a href="#Derivation">prov:Derivation</a>
- </li>
- <li>
- <a href="#PrimarySource">prov:PrimarySource</a>
- </li>
- <li>
- <a href="#Quotation">prov:Quotation</a>
- </li>
- <li>
- <a href="#Revision">prov:Revision</a>
- </li>
- <li>
- <a href="#ActivityInfluence">prov:ActivityInfluence</a>
- </li>
- <li>
- <a href="#Generation">prov:Generation</a>
- </li>
- <li>
- <a href="#Communication">prov:Communication</a>
- </li>
- <li>
- <a href="#Invalidation">prov:Invalidation</a>
- </li>
- <li>
- <a href="#AgentInfluence">prov:AgentInfluence</a>
- </li>
- <li>
- <a href="#Attribution">prov:Attribution</a>
- </li>
- <li>
- <a href="#Association">prov:Association</a>
- </li>
- <li>
- <a href="#Plan">prov:Plan</a>
- </li>
- <li>
- <a href="#Delegation">prov:Delegation</a>
- </li>
- <li>
- <a href="#InstantaneousEvent">prov:InstantaneousEvent</a>
- </li>
- <li>
- <a href="#Role">prov:Role</a>
- </li>
- </ul>
-</div>
-
-<div class="prov-qualified owl-properties at-a-glance">
- <ul class="hlist">
- <li class="object-property">
- <a href="#wasInfluencedBy">prov:wasInfluencedBy</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedInfluence">prov:qualifiedInfluence</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedGeneration">prov:qualifiedGeneration</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedDerivation">prov:qualifiedDerivation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedPrimarySource">prov:qualifiedPrimarySource</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedQuotation">prov:qualifiedQuotation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedRevision">prov:qualifiedRevision</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedAttribution">prov:qualifiedAttribution</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedInvalidation">prov:qualifiedInvalidation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedStart">prov:qualifiedStart</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedUsage">prov:qualifiedUsage</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedCommunication">prov:qualifiedCommunication</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedAssociation">prov:qualifiedAssociation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedEnd">prov:qualifiedEnd</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedDelegation">prov:qualifiedDelegation</a>
- </li>
- <li class="object-property">
- <a href="#influencer">prov:influencer</a>
- </li>
- <li class="object-property">
- <a href="#p_entity">prov:entity</a>
- </li>
- <li class="object-property">
- <a href="#hadUsage">prov:hadUsage</a>
- </li>
- <li class="object-property">
- <a href="#hadGeneration">prov:hadGeneration</a>
- </li>
- <li class="object-property">
- <a href="#p_activity">prov:activity</a>
- </li>
- <li class="object-property">
- <a href="#p_agent">prov:agent</a>
- </li>
- <li class="object-property">
- <a href="#hadPlan">prov:hadPlan</a>
- </li>
- <li class="object-property">
- <a href="#hadActivity">prov:hadActivity</a>
- </li>
- <li class="datatype-property">
- <a href="#atTime">prov:atTime</a>
- </li>
- <li class="object-property">
- <a href="#hadRole">prov:hadRole</a>
- </li>
- </ul>
-</div>
-
- </div>
-
- <div>
-
- </div>
-
- </div> <!-- PROV-O at a glance -->
-
-
-
- <div id="description" class="section">
- <!--OddPage--><h2><span class="secno">3. </span>The PROV-O Ontology Description</h2>
- <p>This section introduces the terms in each of the following categories:
- </p>
- <ul>
- <li><a href="#description-starting-point-terms">Starting Point Terms</a></li>
- <li><a href="#description-expanded-terms">Expanded Terms</a></li>
- <li><a href="#description-qualified-terms">Qualified Terms</a></li>
- </ul>
-
- <div id="description-starting-point-terms" class="section">
- <h3><span class="secno">3.1 </span>Starting Point Terms</h3>
- <p>The Starting Point category is a small set of classes and properties that can be used to create simple, initial provenance descriptions.
- Three classes provide a basis for the rest of PROV-O:
- </p>
- <ul>
- <li>An <a class="qname" href="#Entity">prov:Entity</a> is a physical, digital, conceptual, or other kind of thing with some fixed aspects; entities may be real or imaginary.
- </li>
- <li>An <a class="qname" href="#Activity">prov:Activity</a> is something that occurs over a period of time and acts upon or with entities; it may include consuming, processing, transforming, modifying, relocating, using, or generating entities.
- </li>
- <li>An <a class="qname" href="#Agent">prov:Agent</a> is something that bears some form of responsibility for an activity taking place, for the existence of an entity, or for another agent's activity.
- </li>
- </ul>
- <p>The three primary classes relate to one another and to themselves using the properties shown in the following figure.</p>
-
- <p>Activities <strong>start</strong> and <strong>end</strong> at particular points in time (described using properties
- <a href="#startedAtTime" class="qname">prov:startedAtTime</a> and <a href="#endedAtTime" class="qname">prov:endedAtTime</a>, respectively)
- and during their lifespan can <strong>use</strong> and <strong>generate</strong> a variety of Entities (described with
- <a href="#used" class="qname">prov:used</a> and <a href="#wasGeneratedBy" class="qname">prov:wasGeneratedBy</a>, respectively).
- For example, a blog writing activity may use a particular dataset and generate a bar chart.
- By expressing usage and generation, one can construct provenance chains comprising both Activities and Entities.
- </p>
-
- <p>In addition, we can say that an Activity <a href="#wasInformedBy" class="qname">prov:wasInformedBy</a>
- another Activity to provide some dependency information without explicitly providing the activities' start and end times.
- A <span class="repeated">prov:wasInformedBy</span> relation between Activities suggests that the informed Activity used an Entity that was generated by the informing
- Activity, but the Entity itself is unknown or is not of interest.
- So, the <span class="repeated">prov:wasInformedBy</span> property allows the construction of provenance chains comprising only Activities.
- </p>
-
- <p>Provenance chains comprising only Entities can be formed using the <a href="#wasDerivedFrom" class="qname">prov:wasDerivedFrom</a> property.
- A derivation is a transformation of one entity into another. For example, if the Activity that created the bar chart is not known or is not of interest,
- then we can say that the bar chart <span class="repeated">prov:wasDerivedFrom</span> the dataset.
- Arbitrary RDF properties can be used to describe the fixed aspects of an Entity that are interesting within a particular application (for example,
- the file size and format of the dataset, or the aspect ratio of the bar chart).
- </p>
-
- <p>While the properties <span class="repeated">prov:used</span>, <span class="repeated">prov:wasGeneratedBy</span>,
- <span class="repeated">prov:wasInformedBy</span>, and <span class="repeated">prov:wasDerivedFrom</span> can be used to construct provenance chains among
- Activities and Entities, Agents may also be ascribed responsibility for any Activity or Entity within a provenance chain.
- An Agent's responsibility for an Activity or Entity is described using the properties <a href="#wasAssociatedWith" class="qname">prov:wasAssociatedWith</a> and
- <a href="#wasAttributedTo" class="qname">prov:wasAttributedTo</a>, respectively.
- Agents can also be responsible for other Agents' actions. In this case of delegation, the influencing Agent <a href="#actedOnBehalfOf" class="qname">prov:actedOnBehalfOf</a>
- another Agent that also bears responsibility for the influenced Activity or Entity.
- </p>
-
- <p>The properties rdf:type and rdfs:label are used to express <a href="https://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-type">prov:type</a>
- and <a href="https://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-label">prov:label</a>, respectively.
- </p>
-
- <div id="starting-points-figure" style="text-align: center;" class="figure">
- <!-- When publishing to w3c: replace prov-o-diagrams/ with diagrams/ -->
- <!--img src="prov-o-diagrams/Starting-points-terms.png"-->
- <img src="diagrams/starting-points.svg" style="width: 60%; min-width: 25em; max-width: 60em" alt="PROV-O Starting Point terms">
- <div class="figcaption"><a href="#starting-points-figure">Figure 1</a>.
- The three Starting Point classes and the properties that relate them.<br>
- The diagrams in this document depict Entities as yellow ovals,<br>
- Activities as blue rectangles, and Agents as orange pentagons.<br>
- The responsibility properties are shown in pink.
- </div>
- </div>
-
- <div id="narrative-example-simple-1" class="exampleOuter">
- <p>
- <a href="#narrative-example-simple-1">Example 1</a>: The following PROV-O describes the resources involved when creating a chart about crime statistics. The example uses only Starting Point terms and serves as a basis for elaboration that will be described in subsequent sections. In the example, Derek performs an aggregation of some government crime data, grouping by national regions that are described in a separate dataset by a civil action group.
- </p>
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.org#> .
-
-:bar_chart
- a prov:Entity;
- prov:wasGeneratedBy :illustrationActivity;
- prov:wasDerivedFrom :aggregatedByRegions;
- prov:wasAttributedTo :derek;
-.
-
-:derek
- a foaf:Person, prov:Agent;
- foaf:givenName "Derek";
- foaf:mbox <mailto:derek@example.org>;
- prov:actedOnBehalfOf :natonal_newspaper_inc;
-.
-
-:national_newspaper_inc
- a foaf:Organization, prov:Agent;
- foaf:name "National Newspaper, Inc.";
-.
-
-:illustrationActivity
- a prov:Activity;
- prov:used :aggregatedByRegions;
- prov:wasAssociatedWith :derek;
- prov:wasInformedBy :aggregationActivity;
-.
-
-:aggregatedByRegions
- a prov:Entity;
- prov:wasGeneratedBy :aggregationActivity;
- prov:wasAttributedTo :derek;
-.
-
-:aggregationActivity
- a prov:Activity;
- prov:startedAtTime "2011-07-14T01:01:01Z"^^xsd:dateTime;
- prov:wasAssociatedWith :derek;
- prov:used :crimeData;
- prov:used :nationalRegionsList;
- prov:endedAtTime "2011-07-14T02:02:02Z"^^xsd:dateTime;
-.
-
-:crimeData
- a prov:Entity;
- prov:wasAttributedTo :government;
-.
-:government a foaf:Organization, prov:Agent .
-
-:nationalRegionsList
- a prov:Entity;
- prov:wasAttributedTo :civil_action_group;
-.
-:civil_action_group a foaf:Organization, prov:Agent .</pre>
- </div>
-
- <p>The example states that the agent <code>:derek</code> was associated with two
- activities: <code>:aggregationActivity</code> and <code>:illustrationActivity</code>. The
- activity <code>:aggregationActivity</code> used
- the entities <code>:crimeData</code> (a crime statistics dataset) and <code>:nationalRegionsList</code> (a list of national regions), and
- generated a new entity, <code>:aggregatedByRegions</code> that aggregates the statistics in
- <code>:crimeData</code> according to the regions in <code>:nationalRegionsList</code>.
- The <code>:aggregatedByRegions</code> entity was then used by the <code>:illustrationActivity</code> activity,
- to generate a new entity <code>:bar_chart</code> that depicts the aggregated statistics.
- </p>
-
- <p> The example also states that the activity <code>:illustrationActivity</code> was
- informed by the activity <code>:aggregationActivity</code>. Indeed, the former used
- the entity <code>:aggregatedByRegions</code>, which was generated by the latter.
- </p>
-
- <p> Because the agent <code>:derek</code> was associated with the activities
- <code>:aggregationActivity</code> and <code>:illustrationActivity</code>, the entities
- generated by these activities, i.e., <code>:aggregatedByRegions</code> and <code>:bar_chart</code>, were also
- attributed to him.
- </p>
-
- <p>Finally, the example states that the agent <code>:derek</code> acted on behalf of the organization <code>:national_newspaper_inc</code>.
- </p>
-
- <div id="narrative-example-simple-1-figure" style="text-align: center;" class="figure">
- <img src="diagrams/starting-points-example.svg" style="width: 90%; min-width: 25em; max-width: 60em" alt="Illustration of Derek making a bar chart from some aggregated government data.">
- <div class="figcaption"><a href="#narrative-example-simple-1-figure">Figure 2</a>.
- A graphical illustration of the PROV-O in <a href="#narrative-example-simple-1">Example 1</a>,
- showing how the three Starting Point classes relate.<br>
- The diagrams in this document depict Entities as yellow ovals, Activities as blue rectangles,<br>
- and Agents as orange pentagons. The responsibility properties are shown in pink.
- </div>
- </div>
-
- </div> <!-- Starting Points in PROV-O -->
-
- <div id="description-expanded-terms" class="section">
- <h3><span class="secno">3.2 </span>Expanded Terms</h3>
-
- <p>The terms introduced in this section provide additional ways to describe the provenance among Entities, Activities, and Agents.
- The additional terms are illustrated in the following figure and can be separated into five different categories.</p>
-
- <div id="expanded-terms-figure" style="text-align: center;" class="figure">
- <img src="diagrams/expanded.svg" style="width: 60%; min-width: 25em; max-width: 60em" alt="PROV-O Starting Point terms">
- <div class="figcaption"><a href="#expanded-terms-figure">Figure 3</a>.
- The expanded terms build upon those in the <a href="#description-starting-point-terms">Starting Points section</a>.<br>
- The diagrams in this document depict Entities as yellow ovals, Activities as blue rectangles, and Agents as orange pentagons.<br>
- The domain of <a href="#atLocation">prov:atLocation</a> (<span class="repeated">prov:Activity</span> or <span class="repeated">prov:Entity</span> or <span class="repeated">prov:Agent</span> or <span class="repeated">prov:InstantaneousEvent</span>) is not illustrated.
- </div>
- </div>
-
-
- <p>The <strong>first</strong> category extends the <a href="#description-starting-point-terms">Starting Point terms</a> with subclasses, subproperties, and a superproperty.</p>
-
- <p>Three subclasses of Agent (<a href="#Person" class="qname">prov:Person</a>, <a href="#Organization" class="qname">prov:Organization</a>, and
- <a href="#SoftwareAgent" class="qname">prov:SoftwareAgent</a>) and
- three subclasses of Entity are provided (<a href="#Collection" class="qname">prov:Collection</a>, <a href="#Bundle" class="qname">prov:Bundle</a>,
- and <a href="#Plan" class="qname">prov:Plan</a>).
- </p>
-
- <p>
- A <span class="repeated">prov:Collection</span> is an Entity that provides a structure (e.g. set, list, etc.) to some constituents (which are themselves Entities).
- The <span class="repeated">prov:Collection</span> class can be used to express the provenance of the collection itself:
- e.g. who maintained the collection, which members it contained as it evolved, and how it was assembled.
- The <a href="#hadMember" class="qname">prov:hadMember</a> property is used to assert membership in a collection.
- </p>
-
- <div id="description-bundle">
- <p>
- A <span class="repeated">prov:Bundle</span> is a named set of provenance descriptions, which may itself have provenance.
- The named set of provenance descriptions may be expressed as PROV-O or any other form.
- The subclass of Bundle that names a set of PROV-O assertions is not provided by PROV-O, since it is more appropriate to do so using other recommendations,
- standards, or technologies. In any case, a Bundle of PROV-O assertions is an abstract set of RDF triples, and adding or removing a triple creates a new distinct
- Bundle of PROV-O assertions.
- </p>
- </div>
-
- <p>A <span class="repeated">prov:Plan</span> is an entity that represents a set of actions or steps intended by one or more agents to achieve some goals.
- </p>
-
-
- <p>
- More general and more specific properties are also provided by the expanded terms. More generally, the property
- <a href="#wasInfluencedBy" class="qname">prov:wasInfluencedBy</a> is a superproperty that relates any influenced Entity, Activity, or Agent to any other
- influencing Entity, Activity, or Agent that had an effect on its characteristics.
-
- Three subproperties of <span class="repeated">prov:wasDerivedFrom</span> are also provided for certain kinds of derivation among Entities:
- <a href="#wasQuotedFrom" class="qname">prov:wasQuotedFrom</a> cites a potentially larger Entity (such as a book, blog, or image) from which a new Entity was created
- by repeating some or all of the original,
- <a href="#wasRevisionOf" class="qname">prov:wasRevisionOf</a> indicates that the derived Entity contains substantial content from the original Entity
- (e.g., two editions of a book), and
- <a href="#hadPrimarySource" class="qname">prov:hadPrimarySource</a> cites a preceding Entity produced by some agent with direct experience and
- knowledge about the topic (such as a reading from a sensor, or a journal written during an historical event).
- </p>
-
- <p>The <strong>second</strong> category of expanded terms relates Entities according to their levels of abstraction, where some Entities may present more specific aspects than their more general counterparts.
- While <a href="#specializationOf" class="qname">prov:specializationOf</a> links a more specific Entity to a more general one (e.g., today's BBC news home page versus BBC's news home page on any day), <a href="#alternateOf" class="qname">prov:alternateOf</a> links Entities that present aspects of the same thing, but not necessarily the same aspects or at the same time (e.g., the serialization of a document in different formats or a backup copy of a computer file).
- </p>
-
- <p>
- The <strong>third</strong> category of expanded terms allows further description of Entities. The property <a href="#value" class="qname">prov:value</a>
- provides a literal value that is a direct representation of an entity.
- For example, the <span class="repeated">prov:value</span> of a quote could be a string of the sentences stated, or the <span class="repeated">prov:value</span> of an Entity involved in a numeric calculation could be the xsd:integer four.
- The property <a href="#atLocation" class="qname">prov:atLocation</a> can be used to describe the <a href="#Location" class="qname">prov:Location</a> of any
- Entity, Activity, Agent, or <a href="#InstantaneousEvent" class="qname">prov:InstantaneousEvent</a>
- (i.e., the starting or ending of an activity or the generation, usage, or invalidation of an entity).
- The properties used to describe instances of <span class="repeated">prov:Location</span> are outside the scope of PROV-O;
- reuse of other existing vocabulary is encouraged.
- </p>
-
-
- <p>The <strong>fourth</strong> category of expanded terms describes the lifetime of an Entity beyond being <strong>generated</strong> by an Activity and <strong>used</strong> by other Activities. For example, a painting could not have been displayed before it was painted, and it could not be sold after it was destroyed by fire.
- Similar to how Activities have start and end times, an Entity may be bound by points in time for which it was generated or is no longer usable.
-The properties <a href="#generatedAtTime" class="qname">prov:generatedAtTime</a> and <a href="#invalidatedAtTime" class="qname">prov:invalidatedAtTime</a> can be used to bound the starting and ending moments of an Entity's existence. The Activities that led to the generation or invalidation of an Entity can be provided using <span class="repeated">prov:wasGeneratedBy</span> and <a href="#wasInvalidatedBy" class="qname">prov:wasInvalidatedBy</a>, respectively.
-<a href="#generated" class="qname">prov:generated</a> and <a href="#invalidated" class="qname">prov:invalidated</a> are the inverses of <span class="repeated">prov:wasGeneratedBy</span> and <span class="repeated">prov:wasInvalidatedBy</span>, respectively, and are defined to facilitate Activity-as-subject as well as Entity-as-subject descriptions.
- For more about inverses, see the <a href="#inverse-names">Appendix B</a>.
- </p>
-
- <p>The <strong>fifth</strong> category of expanded terms describes the lifetime of an Activity beyond its start and end times and predecessor Activities.
- Activities may also be started or ended by Entities, which are described using the properties <a href="#wasStartedBy" class="qname">prov:wasStartedBy</a>
- and <a href="#wasEndedBy" class="qname">prov:wasEndedBy</a>, respectively. Since Entities may start or end Activities, and Agents may be Entities,
- then Agents may also start or end Activities.
- </p>
-
- <div id="narrative-example-expanded-1"class="exampleOuter">
- <p>The following examples illustrate the expanded terms by elaborating the <a href="#narrative-example-simple-1">crime chart example</a> from the previous section.
- After aggregating the dataset and creating the chart, Derek published a post to exhibit his work.
- </p>
- <p>
- <a href="#narrative-example-expanded-1">Example 2</a>:
- </p>
-
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix sioc: <http://rdfs.org/sioc/ns#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix my: <http://www.example.org/vocab#> .
-@prefix : <http://www.example.org#> .
-@base <http://www.example.com/derek-bundle.ttl> .
-
-<>
- a prov:Bundle, prov:Entity;
- prov:wasAttributedTo :postEditor;
- prov:generatedAtTime "2011-07-16T02:52:02Z"^^xsd:dateTime;
-.
-
-:derek
- a prov:Person, prov:Agent; ## prov:Agent is inferred from prov:Person
- foaf:givenName "Derek";
- foaf:mbox <mailto:derek@example.org>;
- prov:actedOnBehalfOf :national_newspaper_inc;
-.
-
-:national_newspaper_inc
- a prov:Organization, prov:Agent; ## prov:Agent is inferred from prov:Organization
- foaf:name "National Newspaper, Inc.";
-.
-
-:postEditor
- a prov:SoftwareAgent, prov:Agent; ## prov:Agent is inferred from prov:SoftwareAgent
- foaf:name "Post Editor 3000";
-.
-
-:more-crime-happens-in-cities
- a sioc:Post, prov:Entity;
- sioc:latest_version :post9821v2;
- sioc:previous_version :post9821v1;
-.
-
-## Version 1 of the post
-
-:post9821v1
- a sioc:Post, prov:Entity;
- prov:specializationOf :more-crime-happens-in-cities; ## PERMALINK to the latest revision.
- sioc:title "More crime happens in cities";
- prov:value "I was currius..."; ## The text of this version (with a typo).
- prov:generatedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:wasGeneratedBy :publicationActivity1123;
- prov:wasInfluencedBy :aggregatedByRegions; ## This blog was influenced by Derek's data analysis.
- prov:hadPrimarySource :crimeData; ## Derek's blog derives from the crime data originally
- ## gathered by the government.
- prov:invalidatedAtTime "2011-07-16T02:02:02Z"^^xsd:dateTime;
-.
-
-:publicationActivity1123
- a prov:Activity;
- prov:startedAtTime "2011-07-16T01:01:01Z"^^xsd:dateTime;
- prov:wasStartedBy :derek;
- prov:wasAssociatedWith :postEditor;
- prov:generated :post9821v1;
- prov:endedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:wasEndedBy :derek;
-.
-
-:aggregatedByRegions
- a prov:Entity;
- prov:atLocation <file://Users/aggr.txt>;
-.
-<file://Users/aggr.txt> a prov:Location .
-
-:crimeData
- a prov:Entity;
- prov:wasAttributedTo :government;
-.
-:government
- a prov:Organization, prov:Agent;
-.
-
-## Version 2 of the post
-
-:post9821v2
- a sioc:Post, prov:Entity;
- prov:specializationOf :more-crime-happens-in-cities; ## PERMALINK to the latest revision.
- prov:value "I was curious..."; ## The text of this version (with fixed typo).
- prov:generatedAtTime "2011-07-16T02:02:02Z"^^xsd:dateTime;
- prov:wasRevisionOf :post9821v1;
- prov:alternateOf :post9821v1;
-.</pre>
- </div>
-
- <p>Agent <code>:derek</code>, acting again on behalf of the <code>:national_newspaper_inc</code> organization,
- used the <code>:postEditor</code> tool to publish a post about his recent data analysis <code>:aggregatedByRegions</code>.
- The blog editing tool tracked Derek's actions as PROV-O assertions and published them as a Bundle (the current file <code><></code>).
- The tool recorded that <code>:derek</code> started and ended the publishing activity (<code>:publicationActivity1123</code>)
- that generated the post <code>:post9821v1</code>. The post
- included a permanent link where the content of the latest version is available
- (<code>:more-crime-happens-in-cities</code>) in addition to a textual snapshot of the current version (using prov:value).
- Derek also included additional domain-specific descriptions of the post, such as its title.
- </p>
-
- <p>Shortly after publishing the post, Derek noticed a typographical error in his narrative.
- Because the fix would be minimal, he did not record the activity that led to the new version.
- Instead, he related the new version (<code>:post9821v2</code>) as a revision of the previous (<code>:post9821v1</code>).
- Since both versions of the blog are forms of the long-standing blog permalink <code>:more-crime-happens-in-cities</code>,
- the revisions are alternates of one another and each is a <a href="#specializationOf" class="qname">prov:specializationOf</a> of <code>:more-crime-happens-in-cities</code>.
- </p>
-
- <div id="expanded-example-illustration-1" style="text-align: center;" class="figure">
-
- <img src="diagrams/expanded-terms-example-bundlePost.svg" style="width: 95%; min-width: 25em; max-width: 60em" alt="PROV-O Starting Point terms">
-
- <div class="figcaption"><a href="#expanded-example-illustration-1">Figure 4</a>.
- An illustration of the PROV-O assertions in <a href="#narrative-example-expanded-1">Example 2</a>, where Derek<br>
- published two versions of a blog for the National Newspaper, Inc.<br>
- The diagrams in this document depict Entities as yellow ovals, Activities as blue rectangles,<br>
- and Agents as orange pentagons. The responsibility properties are shown in pink.
- </div>
- </div>
-
-
-
- <div id="narrative-example-expanded-2"class="exampleOuter">
- <p>Shortly after Derek published his blog post, Monica adapted the text for a wider audience in a new post (<code>:post9822</code>).
- This rewrite is an alternate, abbreviated view of the same topic that Derek wrote about and was created from his original text.
- Since the provenance produced by the activities of Derek and Monica corresponded to different user views, the system
- automatically published it in a different <a href="#Bundle" class="qname">prov:Bundle</a>.
- The tool also asserted provenance about the bundle that it produced (e.g., the date of creation, its creator, and the fact that it Derek's bundle was used).
- Because a bundle is a kind of entity, all provenance assertions that can be made about entities can also be made about bundles.
- The use of bundles enables the creation of provenance of provenance.
- </p>
- <p>
- <a href="#narrative-example-expanded-2">Example 3</a>:
- </p>
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix sioc: <http://rdfs.org/sioc/ns#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://www.example.org#> .
-@base <http://www.example.com/monica-bundle.ttl> .
-
-<>
- a prov:Bundle, prov:Entity;
- prov:wasAttributedTo :postEditor;
- prov:wasDerivedFrom <http://www.example.com/derek-bundle.ttl> .
- prov:generatedAtTime "2011-07-16T03:03:03Z"^^xsd:dateTime;
-.
-
-:monica
- a prov:Person, prov:Agent;
- foaf:givenName "Monica";
- foaf:mbox <mailto:monica@example.org>;
-.
-
-## Revised post for a different audience is a new resource.
-
-:post9822
- a sioc:Post, prov:Entity;
- sioc:title "More crime happens in cities (for dummies)";
- prov:wasAttributedTo :monica,
- :postEditor;
- prov:alternateOf :more-crime-happens-in-cities; ## This post is an alternate of Derek's blog.
- prov:value "A quick overview of Derek's..."; ## Snapshot with the content of this version
- prov:wasRevisionOf :post9821v2; ## Monica rewrote Derek's version 2 to create hers.
-.</pre>
- </div>
-
- <div id="narrative-example-expanded-3" class="exampleOuter" >
- <p>After some time, John wrote his own conclusions in his own post (<code>:post19201</code>) quoting the previous two posts.
- Each quote that John makes (<code>:quote_from_monica</code> and <code>:quote_from_derek</code>) is a new entity derived from the
- previous blogs and is annotated with the time that the quote was taken.
- The provenance of John's blog notes that his post is the result of the quotes that he took from Derek and Monica.
- The blog post is also derived from Derek's <code>:aggregatedByRegions</code> dataset because John inspected it and found a
- concern that he discusses in his blog. All the provenance statements related to John's post are grouped in a new <span class="repeated">prov:Bundle</span>.
- </p>
- <p>
- <a href="#narrative-example-expanded-3">Example 4</a>:
- </p>
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix sioc: <http://rdfs.org/sioc/ns#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://www.example.org#> .
-@base <http://www.example.com/john-bundle.ttl> .
-
-<>
- a prov:Bundle, prov:Entity;
- prov:wasAttributedTo :postEditor;
- prov:wasDerivedFrom <http://www.example.com/derek-bundle.ttl>,
- <http://www.example.com/monica-bundle.ttl>;
- prov:generatedAtTime "2012-08-08T08:08:08Z"^^xsd:dateTime;
-.
-
-:publicationActivity1124
- a prov:Activity;
- prov:wasAttributedTo :postEditor,
- :john;
- prov:generated :post19201;
-.
-
-:post19201
- a sioc:Post, prov:Entity;
- prov:wasAttributedTo :john;
- prov:value "I'm not so sure that...";
- prov:wasDerivedFrom :quote_from_derek,
- :quote_from_monica,
- :aggregatedByRegions;
- prov:wasGeneratedBy :publicationActivity1124;
-.
-
-:john
- a prov:Person, prov:Agent;
- foaf:name "John";
-.
-
-:quote_from_derek
- a prov:Entity;
- prov:value "Analysis of the datasets demonstrates that there is more crime.";
- prov:wasQuotedFrom :more-crime-happens-in-cities;
- prov:generatedAtTime "2012-08-08T01:01:01Z"^^xsd:dateTime;
-.
-
-:quote_from_monica
- a prov:Entity;
- prov:value "In summary, there are clearly more crimes in the country.";
- prov:wasQuotedFrom :post9822;
- prov:generatedAtTime "2012-08-08T02:02:02Z"^^xsd:dateTime;
-.</pre>
- </div>
-
-
- <div id="narrative-example-expanded-4" class="exampleOuter" >
- <p>Unfortunately, there was a problem in the servers where <code>:post19201</code> was being stored, and all the data related to the post was lost permanently.
- Thus, the system invalidated the entity automatically and notified John about the error.
- </p>
- <p>
- <a href="#narrative-example-expanded-4">Example 5</a>:
- </p>
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix sioc: <http://rdfs.org/sioc/ns#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.org#> .
-
-:post19201
- a sioc:Post, prov:Entity;
- prov:invalidatedAtTime "2012-09-02T01:31:00Z"^^xsd:dateTime;
- prov:wasInvalidatedBy :hard_disk_failure;
-.
-
-:hard_disk_failure
- a prov:Activity;
- prov:endedAtTime "2012-09-02T01:31:00Z"^^xsd:dateTime;
-.</pre>
- </div>
- </div>
-
-<!-- incorporate https://dvcs.w3.org/hg/prov/rev/e3ecc51f4598 -->
- <div id="description-qualified-terms" class="section">
- <h3><span class="secno">3.3 </span>Qualified Terms</h3>
-
- <p>The Qualified Terms category is the result of
- applying the <strong>Qualification Pattern</strong> [<cite><a class="bibref" rel="biblioentry" href="#bib-LD-Patterns-QR">LD-Patterns-QR</a></cite>] to the simple (unqualified)
- relations available in the <a href="#prov-starting-point-owl-terms-at-a-glance">Starting Point</a> and
- <a href="#prov-expanded-owl-terms-at-a-glance">Expanded</a> categories.
- The terms in this category are for users who wish to provide further details about the provenance-related influence among
- Entities, Activities, and Agents.
- </p>
-
- <p>The Qualification Pattern restates an unqualified influence
- relation by using an intermediate class that represents the influence between two resources.
- This new instance, in turn, can be annotated with additional descriptions of the influence that one resource had upon another.
- The following two tables list the influence relations that can be qualified using the Qualification Pattern, along with the properties used to qualify them.
-
- For example, the second row of the first table indicates that to elaborate how an <span class="repeated">prov:Activity</span>
- <span class="repeated">prov:used</span> a particular <span class="repeated">prov:Entity</span>, one creates an instance of <span class="repeated">prov:Usage</span>
- that indicates the influencing entity with the <span class="repeated">prov:entity</span> property.
- Meanwhile, the influenced <span class="repeated">prov:Activity</span> indicates the <span class="repeated">prov:Usage</span> with the property
- <span class="repeated">prov:qualifiedUsage</span>.
- The resulting structure that qualifies the an Activity's usage of an Entity is illustrated in <a href="#qualified-terms-figure">Figure 4a</a> below.
- </p>
-
- <div id="qualified-forms-starting-point" style="padding: 10px">
- <p>Seven <a href="#description-starting-point-terms">Starting Point</a> relations can be further described using the Qualification Pattern.
- They are listed in the following normative table.
- </p>
- <div style="text-align: center">
- <table class="qualified-forms">
- <caption><a href="#qualified-forms-starting-point">Table 2</a>: Qualification Property and Qualified Influence Class used to qualify a Starting-point Property.</caption>
- <tbody><tr>
- <th><span title="Influenced Class">Influenced Class</span></th>
- <th><span title="Unqualified Influence">Unqualified Influence</span></th>
- <th><span title="Influencing Class">Influencing Class</span></th>
- <th><span title="Qualification Property">Qualification Property</span></th>
- <th><span title="Qualified Influence">Qualified Influence</span></th>
- <th><span title="Influencer Property">Influencer Property</span></th>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy" class="owlproperty">prov:wasGeneratedBy</a></td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedGeneration" href="#qualifiedGeneration" class="owlproperty">prov:qualifiedGeneration</a></td>
- <td><a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlclass">prov:Generation</a></td>
- <td><a title="http://www.w3.org/ns/prov#activity" href="#p_activity" class="owlproperty">prov:activity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlproperty">prov:wasDerivedFrom</a></td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedDerivation" href="#qualifiedDerivation" class="owlproperty">prov:qualifiedDerivation</a></td>
- <td><a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasAttributedTo" href="#wasAttributedTo" class="owlproperty">prov:wasAttributedTo</a></td>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedAttribution" href="#qualifiedAttribution" class="owlproperty">prov:qualifiedAttribution</a></td>
- <td><a title="http://www.w3.org/ns/prov#Attribution" href="#Attribution" class="owlclass">prov:Attribution</a></td>
- <td><a title="http://www.w3.org/ns/prov#agent" href="#p_agent" class="owlproperty">prov:agent</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#used" href="#used" class="owlproperty">prov:used</a></td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedUsage" href="#qualifiedUsage" class="owlproperty">prov:qualifiedUsage</a></td>
- <td><a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlclass">prov:Usage</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasInformedBy" href="#wasInformedBy" class="owlproperty">prov:wasInformedBy</a></td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedCommunication" href="#qualifiedCommunication" class="owlproperty">prov:qualifiedCommunication</a></td>
- <td><a title="http://www.w3.org/ns/prov#Communication" href="#Communication" class="owlclass">prov:Communication</a></td>
- <td><a title="http://www.w3.org/ns/prov#activity" href="#p_activity" class="owlproperty">prov:activity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasAssociatedWith" href="#wasAssociatedWith" class="owlproperty">prov:wasAssociatedWith</a></td>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedAssociation" href="#qualifiedAssociation" class="owlproperty">prov:qualifiedAssociation</a></td>
- <td><a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlclass">prov:Association</a></td>
- <td><a title="http://www.w3.org/ns/prov#agent" href="#p_agent" class="owlproperty">prov:agent</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a></td>
- <td><a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf" class="owlproperty">prov:actedOnBehalfOf</a></td>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation" class="owlproperty">prov:qualifiedDelegation</a></td>
- <td><a title="http://www.w3.org/ns/prov#Delegation" href="#Delegation" class="owlclass">prov:Delegation</a></td>
- <td><a title="http://www.w3.org/ns/prov#agent" href="#p_agent" class="owlproperty">prov:agent</a></td>
- </tr>
-</tbody></table>
-
- </div>
- </div>
-
- <div id="qualified-forms-expanded" style="padding: 10px">
- <p>Seven <a href="#description-expanded-terms">Expanded</a> relations can be further described using the Qualification Pattern.
- They are listed in the following normative table.
- </p>
- <div style="text-align: center">
- <table class="qualified-forms">
- <caption><a href="#qualified-forms-expanded">Table 3</a>: Qualification Property and Qualified Influence Class used to qualify an Expanded Property.</caption>
- <tbody><tr>
- <th><span title="Influenced Class">Influenced Class</span></th>
- <th><span title="Unqualified Influence">Unqualified Influence</span></th>
- <th><span title="Influencing Class">Influencing Class</span></th>
- <th><span title="Qualification Property">Qualification Property</span></th>
- <th><span title="Qualified Influence">Qualified Influence</span></th>
- <th><span title="Influencer Property">Influencer Property</span></th>
- </tr>
- <tr>
- <td style="text-align: center">
- <a title="provEntity" href="#Entity" class="owlclass">prov:Entity</a> or
- <a title="provActivity" href="#Activity" class="owlclass">prov:Activity</a> or
- <a title="provAgent" href="#Agent" class="owlclass">prov:Agent</a> </td>
- <td><a title="provwasInfluencedBy" href="#wasInfluencedBy" class="owlproperty">prov:wasInfluencedBy</a></td>
- <td style="text-align: center">
- <a title="provEntity" href="#Entity" class="owlclass">prov:Entity</a> or
- <a title="provActivity" href="#Activity" class="owlclass">prov:Activity</a> or
- <a title="provAgent" href="#Agent" class="owlclass">prov:Agent</a> </td>
- <td><a title="provqualifiedInfluence" href="#qualifiedInfluence" class="owlproperty">prov:qualifiedInfluence</a></td>
- <td><a title="provInfluence" href="#Influence" class="owlclass">prov:Influence</a></td>
- <td><a title="provinfluencer" href="#influencer" class="owlproperty">prov:influencer</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#hadPrimarySource" href="#hadPrimarySource" class="owlproperty">prov:hadPrimarySource</a></td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedPrimarySource" href="#qualifiedPrimarySource" class="owlproperty">prov:qualifiedPrimarySource</a></td>
- <td><a title="http://www.w3.org/ns/prov#PrimarySource" href="#PrimarySource" class="owlclass">prov:PrimarySource</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasQuotedFrom" href="#wasQuotedFrom" class="owlproperty">prov:wasQuotedFrom</a></td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedQuotation" href="#qualifiedQuotation" class="owlproperty">prov:qualifiedQuotation</a></td>
- <td><a title="http://www.w3.org/ns/prov#Quotation" href="#Quotation" class="owlclass">prov:Quotation</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasRevisionOf" href="#wasRevisionOf" class="owlproperty">prov:wasRevisionOf</a></td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedRevision" href="#qualifiedRevision" class="owlproperty">prov:qualifiedRevision</a></td>
- <td><a title="http://www.w3.org/ns/prov#Revision" href="#Revision" class="owlclass">prov:Revision</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy" class="owlproperty">prov:wasInvalidatedBy</a></td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedInvalidation" href="#qualifiedInvalidation" class="owlproperty">prov:qualifiedInvalidation</a></td>
- <td><a title="http://www.w3.org/ns/prov#Invalidation" href="#Invalidation" class="owlclass">prov:Invalidation</a></td>
- <td><a title="http://www.w3.org/ns/prov#activity" href="#p_activity" class="owlproperty">prov:activity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasStartedBy" href="#wasStartedBy" class="owlproperty">prov:wasStartedBy</a></td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedStart" href="#qualifiedStart" class="owlproperty">prov:qualifiedStart</a></td>
- <td><a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlclass">prov:Start</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasEndedBy" href="#wasEndedBy" class="owlproperty">prov:wasEndedBy</a></td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedEnd" href="#qualifiedEnd" class="owlproperty">prov:qualifiedEnd</a></td>
- <td><a title="http://www.w3.org/ns/prov#End" href="#End" class="owlclass">prov:End</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- </tr>
-</tbody></table>
-
- </div>
- </div>
-
-
- <p>The qualification classes and properties shown in the previous two tables can also be found in the normative <a href="#cross-reference">cross reference</a>
- in the next section of this document.
-
- All influence classes (e.g. <span class="repeated">prov:Association</span>, <span class="repeated">prov:Usage</span>) are extensions of
- <a class="qname" href="#Influence">prov:Influence</a> and either
- <a class="qname" href="#EntityInfluence">prov:EntityInfluence</a>,
- <a class="qname" href="#ActivityInfluence">prov:ActivityInfluence</a>, or
- <a class="qname" href="#AgentInfluence">prov:AgentInfluence</a>, which determine the property used to cite the influencing resource (either
- <a class="qname" href="#p_entity">prov:entity</a>,
- <a class="qname" href="#p_activity">prov:activity</a>, or
- <a class="qname" href="#p_agent">prov:agent</a>, respectively).
- Because <span class="repeated">prov:Influence</span> is a broad relation, its most specific subclasses (e.g. <span class="repeated">prov:Communication</span>,
- <span class="repeated">prov:Delegation</span>, <span class="repeated">prov:End</span>, <span class="repeated">prov:Revision</span>, etc.) should be used when applicable.
-
- </p><div id="narrative-example-qualified-1" class="exampleOuter" >
- <p>
- <a href="#narrative-example-qualified-1">Example 6</a>:
- </p>
- <p>
- For example, given the unqualified statement:
- </p><pre class="example">:e1
- a prov:Entity;
- prov:wasGeneratedBy :a1;
-.
-
-:a1 a prov:Activity .</pre>
- <p></p>
- </div>
-
- <p>One can find that <a class="qname" href="#wasGeneratedBy">prov:wasGeneratedBy</a>
- can be qualified using the qualification property <a class="qname" href="#qualifiedGeneration">prov:qualifiedGeneration</a>,
- the class <a class="qname" href="#Generation">prov:Generation</a> (a subclass of <a class="qname" href="#ActivityInfluence">prov:ActivityInfluence</a>),
- and the property <a class="qname" href="#p_activity">prov:activity</a>.
- From this, the influence relation above can be restated with the <em>qualification pattern</em> as:
- </p>
-
- <div id="narrative-example-qualified-2" class="exampleOuter" >
- <p>
- <a href="#narrative-example-qualified-2">Example 7</a>:
- </p>
- <pre class="example">:e1
- a prov:Entity;
- prov:wasGeneratedBy :a1;
- prov:qualifiedGeneration :e1Gen; # Add the qualification.
-.
-
-:e1Gen
- a prov:Generation;
- prov:activity :a1; # Cite the influencing Activity.
- ex:foo :bar; # Describe the Activity :a1's influence upon the Entity :e1.
-.
-
-:a1 a prov:Activity .</pre>
- </div>
-
- <p>
- The asserter can thus attach additional properties to <code>:e1Gen</code> to describe the generation of <code>:e1</code> by <code>:a1</code>.
- </p>
-
- <p>
- As can be seen in this example, qualifying an influence relation provides a second form (e.g. <code>:e1 prov:qualifiedGeneration :e1Gen</code>) to express an equivalent influence relation
- (e.g. <code>:e1 prov:wasGeneratedBy :a1</code>).
- It is correct and acceptable for an implementer to use either qualified or unqualified forms as they choose (or both),
- and a consuming application should be prepared to recognize either form.
- Consuming applications <em class="rfc2119" title="should">should</em> recognize both qualified and unqualified forms, and treat the qualified form as implying the unqualified form.
- Because the qualification form is more verbose, the unqualified form should be favored in cases where additional properties are not provided.
- When the qualified form is expressed, including the equivalent unqualified form can facilitate PROV-O consumption, and is thus encouraged.
- </p>
- <!-- To simplify client queries,
- any qualified relation SHOULD be accompanied by the equivalent unqualified statement.
- Unqualified properties SHOULD NOT have the equivalent qualified form
- asserted unless it adds additional information. -->
-
- <p>In addition to the previous two tables, <a href="#qualified-terms-figure">Figure 4</a>
- illustrates the classes and properties needed to apply the qualification pattern to ten of the fourteen qualifiable influence relations.
-
- For example, while <a class="qname" href="#qualifiedUsage">prov:qualifiedUsage</a>,
- <a class="qname" href="#Usage">prov:Usage</a>, and <a class="qname" href="#p_entity">prov:entity</a> are used to qualify
- <span class="repeated">prov:used</span> relations,
-
- <a class="qname" href="#qualifiedAssociation">prov:qualifiedAssociation</a>, <a class="qname" href="#Association">prov:Association</a>,
- and <a class="qname" href="#p_agent">prov:agent</a> are used to qualify <span class="repeated">prov:wasAssociatedWith</span>
- relations. This pattern applies to the twelve other influence relations that can be qualified.
- </p>
-
- <p>In subfigure <strong>a</strong> the <span class="repeated">prov:qualifiedUsage</span> property parallels the <span class="repeated">prov:used</span> property and references an instance of
- <span class="repeated">prov:Usage</span>, which in turn provides attributes of the <span class="repeated">prov:used</span> relation between the Activity and Entity.
- The <span class="repeated">prov:entity</span> property is used to cite the Entity that was used by the Activity.
- In this case, the time that the Activity used the Entity is provided using the <a href="#atTime" class="qname">prov:atTime</a> property and a literal
- <span class="repeated">xsd:dateTime</span> value. The <span class="repeated">prov:atTime</span> property can be used to describe any
- <a href="#InstantaneousEvent" class="qname">prov:InstantaneousEvent</a> (including
- <a href="#Start" class="qname">prov:Start</a>,
- <a href="#Generation" class="qname">prov:Generation</a>,
- <a href="#Usage" class="qname">prov:Usage</a>,
- <a href="#Invalidation" class="qname">prov:Invalidation</a>, and
- <a href="#End" class="qname">prov:End</a>).
- </p>
-
- <p>Similarly in subfigure <strong>j</strong>, the <span class="repeated">prov:qualifiedAssociation</span> property parallels the
- <span class="repeated">prov:wasAssociatedWith</span> property and references an instance of
- <span class="repeated">prov:Association</span>, which in turn provides attributes of the
- <span class="repeated">prov:wasAssociatedWith</span> relation between the Activity and Agent. The
- <span class="repeated">prov:agent</span> property is used to cite the Agent that influenced the Activity.
- In this case, the plan of actions and steps that the Agent used to achieve its goals is provided using the
- <a href="#hadPlan" class="qname">prov:hadPlan</a> property and an instance of <a href="#Plan" class="qname">prov:Plan</a>. Further, the
- <a href="#hadRole" class="qname">prov:hadRole</a> property and <a href="#Role" class="qname">prov:Role</a>
- class can be used to describe the function that the agent served with respect to the Activity.
- Both <span class="repeated">prov:Plan</span> and <span class="repeated">prov:Role</span> are left to be extended by applications.
- </p>
-
- <div id="qualified-terms-figure" style="text-align: center;" class="figure">
- <!-- When publishing to w3c: replace prov-o-diagrams/ with diagrams/ -->
- <!--img src="prov-o-diagrams/Qualified-Association.png"-->
- <img src="diagrams/qualified-patterns.svg" style="width: 70%; min-width: 25em; max-width: 70em" alt="Express association between an activity and an agent using a binary relationship and an alternatie qualified relationship">
- <div class="figcaption"><a href="#qualified-terms-figure">Figure 4</a>:
- Illustration of the properties and classes to use (<span style="color: blue">in blue</span>)
- to qualify the
- <a href="#description-starting-point-terms">starting point</a> and
- <a href="#description-expanded-terms">expanded</a> influence relations (<strong>dotted black</strong>). <br>
- The diagrams in this document depict Entities as ovals, Activities as rectangles, and Agents as pentagons.
- <a href="#Quotation">Quotation</a>, <a href="#Revision">Revision</a>, and <a href="#PrimarySource">PrimarySource</a>
- are omitted because they are special forms of <a href="#Derivation">Derivation</a> and follow the same pattern as subfigure <strong>g</strong>.</div>
- </div>
-
-
-
-
- <p>The following two examples show the result of applying the Usage and Association patterns to the chart-making example from <a href="#description-starting-point-terms">Section 3.1</a>.
- </p>
-
- <div id="narrative-example-qualified-3" class="exampleOuter" >
- <p>
- <a href="#narrative-example-qualified-3">Example 8</a>:
- </p>
- <div class="exampleOuter">
- <div><b>Qualified Usage</b></div>
- <p>The <span class="repeated">prov:qualifiedUsage</span> property parallels the <span class="repeated">prov:used</span> property to provide an additional description to <code>:illustrationActivity</code>. The instance of <span class="repeated">prov:Usage</span> cites the data used (<code>:aggregatedByRegions</code>) and the time the activity used it (<code>2011-07-14T03:03:03Z</code>).
- </p>
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.org#> .
-
-:illustrationActivity
- a prov:Activity; ## Using Starting Point terms,
- prov:used :aggregatedByRegions; ## the illustration activity used the aggregated data (to create the bar chart).
-.
-
-:aggregatedByRegions a prov:Entity .
-
-:illustrationActivity
- prov:qualifiedUsage [ ## Qualify how the :illustrationActivity
- a prov:Usage; ## used
- prov:entity :aggregatedByRegions; ## the Entity :aggregatedByRegions
-
- prov:atTime "2011-07-14T03:03:03Z"^^xsd:dateTime; ## Qualification: The aggregated data was used
- ## at a particular time to create the bar chart..
- ];
-.</pre>
- </div>
- </div>
-
- <div id="narrative-example-qualified-4" class="exampleOuter" >
- <p>
- <a href="#narrative-example-qualified-4">Example 9</a>:
- </p>
- <div class="exampleOuter">
- <div><b>Qualified Association</b></div>
- <p>The <span class="repeated">prov:qualifiedAssociation</span> property parallels the
- <span class="repeated">prov:wasAssociatedWith</span> property to provide an additional description about the <code>:illustrationActivity</code> that Derek influenced.
- The instance of <span class="repeated">prov:Association</span> cites the influencing agent (<code>:derek</code>) that followed the instructions (<code>:tutorial_blog</code>).
- Further, Derek served the role of <code>:illustrationist</code> during the activity.
- </p>
- <pre class="example">@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.org#> .
-
-:illustrationActivity
- a prov:Activity; ## Using Starting Point terms,
- prov:wasAssociatedWith :derek; ## the illustration activity was associated with Derek in some way.
-.
-
-:derek a prov:Agent .
-
-:illustrationActivity
- prov:qualifiedAssociation [ ## Qualify how the :illustrationActivity
- a prov:Association; ## was associated with
- prov:agent :derek ## the Agent Derek.
-
- prov:hadRole :illustrationist; ## Qualification: The role that Derek served.
- prov:hadPlan :tutorial_blog; ## Qualification: The plan (or recipe, instructions)
- ## that Derek followed when creating the graphical chart.
- ];
-.
-
-:tutorial_blog a prov:Plan, prov:Entity .
-:illustrationist a prov:Role .</pre>
- </div>
- </div>
-
-
- <p>This section finishes with two more examples of qualification as applied to the chart-making example from <a href="#description-starting-point-terms">Section 3.1</a>.
- </p>
-
-
- <div id="narrative-example-qualified-5" class="exampleOuter" >
- <p>
- <a href="#narrative-example-qualified-5">Example 10</a>:
- </p>
- <div class="exampleOuter">
- <div><b>Qualified Generation</b></div>
- <p>The <span class="repeated">prov:qualifiedGeneration</span> property parallels the <span class="repeated">prov:wasGeneratedBy</span> property to provide an additional description to <code>:bar_chart</code>. The instance of <span class="repeated">prov:Generation</span> cites the time (2011-07-14T15:52:14Z) that the activity (<code>:illustrationActivity</code>) generated the chart (<code>:bar_chart</code>).
- </p>
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.org#> .
-
-:bar_chart
- a prov:Entity; ## Using Starting Point terms,
- prov:wasGeneratedBy :illustrationActivity; ## the chart was generated in an illustration activity.
-.
-
-:illustrationActivity a prov:Activity .
-
-:bar_chart
- prov:qualifiedGeneration [ ## Qualify how the :bar_chart
- a prov:Generation; ## was generated by
- prov:activity :illustrationActivity; ## the Activity :illustrationActivity.
-
- prov:atTime "2011-07-14T15:52:14Z"^^xsd:dateTime; ## Qualification: The Activity generated
- ## the bar_chart at a particular time.
- ];
-.</pre>
- </div>
- </div>
-
- <div id="narrative-example-qualified-6" class="exampleOuter" >
- <p>
- <a href="#narrative-example-qualified-6">Example 11</a>:
- </p>
- <div class="exampleOuter">
- <div><b>Qualified Derivation</b></div>
- <p>The <span class="repeated">prov:qualifiedDerivation</span> property parallels the <span class="repeated">prov:wasDerivedFrom</span>
- property to provide an additional description to <code>:bar_chart</code>. The instance of <span class="repeated">prov:Derivation</span>
- cites the activity (<code>:illustrationActivity</code>) and the Usages and Generations that the activity conduced to create the <code>:bar_chart</code>.
- </p>
- <pre class="example">@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.org#> .
-
-:bar_chart
- a prov:Entity; ## Using Starting Point terms,
- prov:wasDerivedFrom :aggregatedByRegions; ## the chart was derived from the aggregated dataset.
-.
-
-:aggregatedByRegions a prov:Entity .
-
-:bar_chart
- prov:qualifiedDerivation [ ## Qualify
- a prov:Derivation; ## how :bar_chart was derived from
- prov:entity :aggregatedByRegions; ## the dataset Entity :aggregatedByRegions.
-
- prov:hadActivity :aggregating_activity; ## Qualification: The activity that derived the :bar_chart.
- prov:hadUsage :use_of_aggregatedData; ## Qualification: How the activity used :aggregatedByRegions.
- prov:hadGeneration :generation_of_bar_chart; ## Qualification: How the activity generated the :bar_chart.
- ];
-.</pre>
- </div>
- </div>
-
- </div>
-
-
- </div>
-
-
-
- <div id="cross-reference" class="normative section">
- <!-- prov:tracedTo [ prov:wasGeneratedBy [ a prov:Activity;
- dcterms:description "python eg-24-prov-o-html-examples.py http://dvcs.w3.org/hg/prov/raw-file/default/ontology/ProvenanceOntology.owl" ] ] ] -->
- <!--OddPage--><h2><span class="secno">4. </span>Cross reference for PROV-O classes and properties</h2>
- <p>This section provides details for each class and property defined by the PROV Ontology, grouped by the categories described above:
- </p>
- <ul>
- <li><a href="#cross-reference-starting-point-terms">Starting Point Terms</a></li>
- <li><a href="#cross-reference-expanded-terms">Expanded Terms</a></li>
- <li><a href="#cross-reference-qualified-terms">Qualified Terms</a></li>
- </ul>
-
- <p>
- The superscripts <sup class="type-op" title="object property">op</sup> and <sup class="type-dp" title="data property">dp</sup> denote that a property is an OWL <a href="http://www.w3.org/TR/owl2-syntax/#Object_Properties">object property</a> or <a href="http://www.w3.org/TR/owl2-syntax/#Data_Properties">data property</a>, respectively.
- </p>
-
- <p>Each PROV-O term in this cross reference links to the corresponding PROV-DM concept. The PROV-DM's table
- <a href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#prov-dm-to-prov-o-and-prov-n">Cross-References to PROV-O and PROV-N</a>
- provides an overview of the correspondences between PROV-O and PROV-DM.
-
- </p>
-
- <p>
- The qualification classes and properties shown in <a href="#qualified-forms-starting-point">Table 2</a> and
- <a href="#qualified-forms-expanded">Table 3</a> of the previous section can also be found in each entry of this cross reference.
- If the property can be qualified, the <strong>can be qualified with</strong>
- header indicates the qualifying property and influence class that should be used.
- Conversely, the <strong>qualifies</strong> headers in the listings for qualification terms indicate the unqualified property that they qualify.
- In the OWL file itself, the annotation properties <span class="qname repeated">prov:qualifiedForm</span> and <span class="qname repeated">prov:unqualifiedForm</span>
- provide the same linkages between the unqualified properties and their qualifiying terms.
- </p>
-
- <p>Most examples shown in this cross reference are encoded using the Turtle RDF serialization.
- When it is convenient to do so (e.g., when an example describes a <span class="qname repeated">prov:Bundle</span>), it may use the [<cite><a class="bibref" rel="biblioentry" href="#bib-TRIG">TRIG</a></cite>] syntax.
- Although this document does not specify how to encode Bundles in RDF, TriG's named graph construct is used only to illustrate the concept of
- creating a named set of PROV assertions. Note that <a href="#compliance">all examples are non-normative</a>.
- </p>
-
- <div id="cross-reference-starting-point-terms" class="section">
- <h3><span class="secno">4.1 </span>Starting Point Terms</h3>
- <p>The classes and properties that provide a basis for all other PROV-O terms are discussed in <a href="#description-starting-point-terms">Section 3.1</a>.</p>
-
-<div class="prov-starting-point owl-classes at-a-glance">
- <ul class="hlist">
- <li>
- <a href="#Entity">prov:Entity</a>
- </li>
- <li>
- <a href="#Activity">prov:Activity</a>
- </li>
- <li>
- <a href="#Agent">prov:Agent</a>
- </li>
- </ul>
-</div>
-
-<div class="prov-starting-point owl-properties at-a-glance">
- <ul class="hlist">
- <li class="object-property">
- <a href="#wasGeneratedBy">prov:wasGeneratedBy</a>
- </li>
- <li class="object-property">
- <a href="#wasDerivedFrom">prov:wasDerivedFrom</a>
- </li>
- <li class="object-property">
- <a href="#wasAttributedTo">prov:wasAttributedTo</a>
- </li>
- <li class="datatype-property">
- <a href="#startedAtTime">prov:startedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#used">prov:used</a>
- </li>
- <li class="object-property">
- <a href="#wasInformedBy">prov:wasInformedBy</a>
- </li>
- <li class="datatype-property">
- <a href="#endedAtTime">prov:endedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#wasAssociatedWith">prov:wasAssociatedWith</a>
- </li>
- <li class="object-property">
- <a href="#actedOnBehalfOf">prov:actedOnBehalfOf</a>
- </li>
- </ul>
-</div>
-
- <div class="prov-starting-point owl-classes crossreference">
-
- <div id="Entity" class="entity">
- <h3 id="x1--------class--prov-entity-----------------back-to-starting-point-classes">
- <span class="xref" id="eg1">(1)</span>
- Class: <a href="#Entity"><span class="dotted" title="http://www.w3.org/ns/prov#Entity">prov:Entity</span></a>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Entity</p>
- <div class="definition"><p>An entity is a physical, digital, conceptual, or other kind of thing with some fixed aspects; entities may be real or imaginary. </p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix dcterms: <http://purl.org/dc/terms/> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:bar_chart
- a prov:Entity;
- dcterms:title "Aggregated statistics from the crime file"^^xsd:string;
- prov:wasAttributedTo :derek;
-.
-
-:derek a prov:Agent .
-</pre>
- </div>
-
- <dl class="description">
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#invalidatedAtTime" href="#invalidatedAtTime">prov:invalidatedAtTime</a> <sup class="type-dp" title="data property">dp</sup>
- , <a title="http://www.w3.org/ns/prov#wasAttributedTo" href="#wasAttributedTo">prov:wasAttributedTo</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedGeneration" href="#qualifiedGeneration">prov:qualifiedGeneration</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy">prov:wasGeneratedBy</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom">prov:wasDerivedFrom</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#specializationOf" href="#specializationOf">prov:specializationOf</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedDerivation" href="#qualifiedDerivation">prov:qualifiedDerivation</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedInvalidation" href="#qualifiedInvalidation">prov:qualifiedInvalidation</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#generatedAtTime" href="#generatedAtTime">prov:generatedAtTime</a> <sup class="type-dp" title="data property">dp</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedQuotation" href="#qualifiedQuotation">prov:qualifiedQuotation</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#hadPrimarySource" href="#hadPrimarySource">prov:hadPrimarySource</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedPrimarySource" href="#qualifiedPrimarySource">prov:qualifiedPrimarySource</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#alternateOf" href="#alternateOf">prov:alternateOf</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#value" href="#value">prov:value</a> <sup class="type-dp" title="data property">dp</sup>
- , <a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy">prov:wasInvalidatedBy</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedAttribution" href="#qualifiedAttribution">prov:qualifiedAttribution</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasQuotedFrom" href="#wasQuotedFrom">prov:wasQuotedFrom</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedRevision" href="#qualifiedRevision">prov:qualifiedRevision</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasRevisionOf" href="#wasRevisionOf">prov:wasRevisionOf</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#atLocation" href="#atLocation">prov:atLocation</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadPrimarySource" href="#hadPrimarySource">prov:hadPrimarySource</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#generated" href="#generated">prov:generated</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom">prov:wasDerivedFrom</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#entity" href="#p_entity">prov:entity</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#specializationOf" href="#specializationOf">prov:specializationOf</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#invalidated" href="#invalidated">prov:invalidated</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#used" href="#used">prov:used</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#hadMember" href="#hadMember">prov:hadMember</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#alternateOf" href="#alternateOf">prov:alternateOf</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasStartedBy" href="#wasStartedBy">prov:wasStartedBy</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasQuotedFrom" href="#wasQuotedFrom">prov:wasQuotedFrom</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasEndedBy" href="#wasEndedBy">prov:wasEndedBy</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasRevisionOf" href="#wasRevisionOf">prov:wasRevisionOf</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Collection" href="#Collection" class="owlclass">prov:Collection</a>
- , <a title="http://www.w3.org/ns/prov#Plan" href="#Plan" class="owlclass">prov:Plan</a>
- , <a title="http://www.w3.org/ns/prov#Bundle" href="#Bundle" class="owlclass">prov:Bundle</a>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-entity">entity</a> </dd>
- </dl>
- </div>
-
- <div id="Activity" class="entity">
- <h3 id="x2--------class--prov-activity-----------------back-to-starting-point-classes">
- <span class="xref" id="eg2">(2)</span>
- Class: <a href="#Activity"><span class="dotted" title="http://www.w3.org/ns/prov#Activity">prov:Activity</span></a>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Activity</p>
- <div class="definition"><p>An activity is something that occurs over a period of time and acts upon or with entities; it may include consuming, processing, transforming, modifying, relocating, using, or generating entities.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:graduation
- a prov:Activity, :Graduation;
- prov:startedAtTime "2012-04-15T13:00:00-04:00"^^xsd:dateTime;
- prov:used :ms_smith;
- prov:generated :doctor_smith;
- prov:endedAtTime "2012-04-15T14:30:00-04:00"^^xsd:dateTime;
-.
-:ms_smith a prov:Entity .
-:doctor_smith a prov:Entity .
-</pre>
- </div>
-
- <dl class="description">
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#generated" href="#generated">prov:generated</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedAssociation" href="#qualifiedAssociation">prov:qualifiedAssociation</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasAssociatedWith" href="#wasAssociatedWith">prov:wasAssociatedWith</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedEnd" href="#qualifiedEnd">prov:qualifiedEnd</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasEndedBy" href="#wasEndedBy">prov:wasEndedBy</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedUsage" href="#qualifiedUsage">prov:qualifiedUsage</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#used" href="#used">prov:used</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#invalidated" href="#invalidated">prov:invalidated</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#endedAtTime" href="#endedAtTime">prov:endedAtTime</a> <sup class="type-dp" title="data property">dp</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedStart" href="#qualifiedStart">prov:qualifiedStart</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasInformedBy" href="#wasInformedBy">prov:wasInformedBy</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#wasStartedBy" href="#wasStartedBy">prov:wasStartedBy</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#startedAtTime" href="#startedAtTime">prov:startedAtTime</a> <sup class="type-dp" title="data property">dp</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedCommunication" href="#qualifiedCommunication">prov:qualifiedCommunication</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#atLocation" href="#atLocation">prov:atLocation</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#activity" href="#p_activity">prov:activity</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasInformedBy" href="#wasInformedBy">prov:wasInformedBy</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy">prov:wasGeneratedBy</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy">prov:wasInvalidatedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Activity">Activity</a> </dd>
- </dl>
- </div>
-
- <div id="Agent" class="entity">
- <h3 id="x3--------class--prov-agent-----------------back-to-starting-point-classes">
- <span class="xref" id="eg3">(3)</span>
- Class: <a href="#Agent"><span class="dotted" title="http://www.w3.org/ns/prov#Agent">prov:Agent</span></a>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Agent</p>
- <div class="definition"><p>An agent is something that bears some form of responsibility for an activity taking place, for the existence of an entity, or for another agent's activity. </p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix : <http://example.com#> .
-
-:derek
- a prov:Agent, prov:Person;
- foaf:givenName "Derek"^^xsd:string;
- foaf:mbox <mailto:derek@example.org>;
- foaf:homePage <http://derek.example.com>;
- prov:actedOnBehalfOf :national_newspaper_inc;
-.
-
-:national_newspaper_inc
- a prov:Agent, prov:Organization;
- foaf:name "National Newspaper, Inc.";
-.
-</pre>
- </div>
-
- <dl class="description">
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf">prov:actedOnBehalfOf</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation">prov:qualifiedDelegation</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#atLocation" href="#atLocation">prov:atLocation</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf">prov:actedOnBehalfOf</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#agent" href="#p_agent">prov:agent</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasAssociatedWith" href="#wasAssociatedWith">prov:wasAssociatedWith</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#wasAttributedTo" href="#wasAttributedTo">prov:wasAttributedTo</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Organization" href="#Organization" class="owlclass">prov:Organization</a>
- , <a title="http://www.w3.org/ns/prov#Person" href="#Person" class="owlclass">prov:Person</a>
- , <a title="http://www.w3.org/ns/prov#SoftwareAgent" href="#SoftwareAgent" class="owlclass">prov:SoftwareAgent</a>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-agent">agent</a> </dd>
- </dl>
- </div>
-</div>
-<div class="prov-starting-point owl-properties crossreference" >
- <div id="wasGeneratedBy" class="entity">
- <h3 id="x4--------property--prov-wasgeneratedby-op-----------------back-to-starting-point-properties">
- <span class="xref" id="eg4">(4)</span>
- Property: <a href="#wasGeneratedBy"><span class="dotted" title="http://www.w3.org/ns/prov#wasGeneratedBy">prov:wasGeneratedBy</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasGeneratedBy</p>
- <div class="definition def-from-5"><p>Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:bar_chart
- a prov:Entity;
- prov:wasGeneratedBy :illustrating;
-.
-
-:illustrating a prov:Activity .
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlclass">prov:Generation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedGeneration" href="#qualifiedGeneration" class="owlproperty">prov:qualifiedGeneration</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Generation">Generation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasDerivedFrom" class="entity">
- <h3 id="x5--------property--prov-wasderivedfrom-op-----------------back-to-starting-point-properties">
- <span class="xref" id="eg5">(5)</span>
- Property: <a href="#wasDerivedFrom"><span class="dotted" title="http://www.w3.org/ns/prov#wasDerivedFrom">prov:wasDerivedFrom</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasDerivedFrom</p>
- <div class="definition def-from-1"><p>A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:bar_chart
- a prov:Entity, ex:Barchart;
- prov:wasDerivedFrom :aggregatedByRegions;
-.
-
-:aggregatedByRegions
- a prov:Entity, ex:Dataset;
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The more specific subproperties of prov:wasDerivedFrom (i.e., prov:wasQuotedFrom, prov:wasRevisionOf, prov:hadPrimarySource) should be used when applicable.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has sub-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#hadPrimarySource" href="#hadPrimarySource" class="owlclass">prov:hadPrimarySource</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasQuotedFrom" href="#wasQuotedFrom" class="owlclass">prov:wasQuotedFrom</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasRevisionOf" href="#wasRevisionOf" class="owlclass">prov:wasRevisionOf</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedDerivation" href="#qualifiedDerivation" class="owlproperty">prov:qualifiedDerivation</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Derivation">Derivation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasAttributedTo" class="entity">
- <h3 id="x6--------property--prov-wasattributedto-op-----------------back-to-starting-point-properties">
- <span class="xref" id="eg6">(6)</span>
- Property: <a href="#wasAttributedTo"><span class="dotted" title="http://www.w3.org/ns/prov#wasAttributedTo">prov:wasAttributedTo</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasAttributedTo</p>
- <div class="definition def-from-1"><p>Attribution is the ascribing of an entity to an agent.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:geneSequencing
- a prov:Activity;
- prov:startedAtTime "2012-04-25T01:30:00Z"^^xsd:dateTime;
- prov:used :drosophilaSample-84;
- prov:wasAssociatedWith :lab-technician-GH-32;
- prov:endedAtTime "2012-04-25T03:40:00Z"^^xsd:dateTime;
-.
-
-:drosophilaSample-84
- a prov:Entity;
- prov:wasAttributedTo :lab-technician-FE-56;
-.
-
-:lab-technician-GH-32 a prov:Agent .
-:lab-technician-FE-56 a prov:Agent .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>Attribution is the ascribing of an entity to an agent.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedAttribution" href="#qualifiedAttribution" class="owlproperty">prov:qualifiedAttribution</a> <sup class="type-op" title="object property">op</sup>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#Attribution" href="#Attribution" class="owlclass">prov:Attribution</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribution">attribution</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="startedAtTime" class="entity">
- <h3 id="x7--------property--prov-startedattime-dp-----------------back-to-starting-point-properties">
- <span class="xref" id="eg7">(7)</span>
- Property: <a href="#startedAtTime"><span class="dotted" title="http://www.w3.org/ns/prov#startedAtTime">prov:startedAtTime</span></a> <sup class="type-dp" title="data property">dp</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#startedAtTime</p>
- <div class="definition def-from-5"><p>Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:geneSequencing
- a prov:Activity;
- prov:startedAtTime "2012-04-25T01:30:00Z"^^xsd:dateTime;
- prov:used :drosophilaSample-84;
- prov:wasAssociatedWith :lab-technician-GH-32;
- prov:endedAtTime "2012-04-25T03:40:00Z"^^xsd:dateTime;
-.
-
-:drosophilaSample-84 a prov:Entity .
-:lab-technician-GH-32 a prov:Agent .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The time at which an activity started. See also prov:endedAtTime.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- http://www.w3.org/2001/XMLSchema#dateTime
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlclass">prov:Start</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime" class="owlproperty">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Start">Start</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="used" class="entity">
- <h3 id="x8--------property--prov-used-op-----------------back-to-starting-point-properties">
- <span class="xref" id="eg8">(8)</span>
- Property: <a href="#used"><span class="dotted" title="http://www.w3.org/ns/prov#used">prov:used</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#used</p>
- <div class="definition def-from-5"><p>Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:sortActivity
- a prov:Activity;
- prov:atTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:used :datasetA;
- prov:generated :datasetB;
-.
-
-:datasetA a prov:Entity.
-:datasetB a prov:Entity.
-
-# See qualified Usage for example on how the role of :datasetA can be described for this Activity
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>A prov:Entity that was used by this prov:Activity. For example, :baking prov:used :spoon, :egg, :oven .</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlclass">prov:Usage</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedUsage" href="#qualifiedUsage" class="owlproperty">prov:qualifiedUsage</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Usage">Usage</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasInformedBy" class="entity">
- <h3 id="x9--------property--prov-wasinformedby-op-----------------back-to-starting-point-properties">
- <span class="xref" id="eg9">(9)</span>
- Property: <a href="#wasInformedBy"><span class="dotted" title="http://www.w3.org/ns/prov#wasInformedBy">prov:wasInformedBy</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasInformedBy</p>
- <div class="definition def-from-5"><p>Communication is the exchange of an entity by two activities, one activity using the entity generated by the other.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:writing-celebrity-gossip
- a prov:Activity;
- prov:wasInformedBy :voicemail-interception;
-.
-
-:voicemail-interception a prov:Activity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>An activity a2 is dependent on or informed by another activity a1, by way of some unspecified entity that is generated by a1 and used by a2.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Communication" href="#Communication" class="owlclass">prov:Communication</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedCommunication" href="#qualifiedCommunication" class="owlproperty">prov:qualifiedCommunication</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Communication">Communication</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="endedAtTime" class="entity">
- <h3 id="x10--------property--prov-endedattime-dp-----------------back-to-starting-point-properties">
- <span class="xref" id="eg10">(10)</span>
- Property: <a href="#endedAtTime"><span class="dotted" title="http://www.w3.org/ns/prov#endedAtTime">prov:endedAtTime</span></a> <sup class="type-dp" title="data property">dp</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#endedAtTime</p>
- <div class="definition def-from-5"><p>End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:geneSequencing
- a prov:Activity;
- prov:startedAtTime "2012-04-25T01:30:00Z"^^xsd:dateTime;
- prov:used :drosophilaSample-84;
- prov:wasAssociatedWith :lab-technician-GH-32;
- prov:endedAtTime "2012-04-25T03:40:00Z"^^xsd:dateTime;
-.
-
-:drosophilaSample-84 a prov:Entity .
-:lab-technician-GH-32 a prov:Agent .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The time at which an activity ended. See also prov:startedAtTime.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- http://www.w3.org/2001/XMLSchema#dateTime
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#End" href="#End" class="owlclass">prov:End</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime" class="owlproperty">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-End">End</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasAssociatedWith" class="entity">
- <h3 id="x11--------property--prov-wasassociatedwith-op-----------------back-to-starting-point-properties">
- <span class="xref" id="eg11">(11)</span>
- Property: <a href="#wasAssociatedWith"><span class="dotted" title="http://www.w3.org/ns/prov#wasAssociatedWith">prov:wasAssociatedWith</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasAssociatedWith</p>
- <div class="definition def-from-5"><p>An activity association is an assignment of responsibility to an agent for an activity, indicating that the agent had a role in the activity. It further allows for a plan to be specified, which is the plan intended by the agent to achieve some goals in the context of this activity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrating
- a prov:Activity;
- prov:wasAssociatedWith :derek;
-.
-
-:derek a prov:Person, prov:Agent, prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>An prov:Agent that had some (unspecified) responsibility for the occurrence of this prov:Activity.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlclass">prov:Association</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedAssociation" href="#qualifiedAssociation" class="owlproperty">prov:qualifiedAssociation</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Association">Association</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="actedOnBehalfOf" class="entity">
- <h3 id="x12--------property--prov-actedonbehalfof-op-----------------back-to-starting-point-properties">
- <span class="xref" id="eg12">(12)</span>
- Property: <a href="#actedOnBehalfOf"><span class="dotted" title="http://www.w3.org/ns/prov#actedOnBehalfOf">prov:actedOnBehalfOf</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-starting-point-owl-terms-at-a-glance">starting-point properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#actedOnBehalfOf</p>
- <div class="definition def-from-5"><p>Delegation is the assignment of authority and responsibility to an agent (by itself or by another agent) to carry out a specific activity as a delegate or representative, while the agent it acts on behalf of retains some responsibility for the outcome of the delegated work.
-
-For example, a student acted on behalf of his supervisor, who acted on behalf of the department chair, who acted on behalf of the university; all those agents are responsible in some way for the activity that took place but we do not say explicitly who bears responsibility and to what degree.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:derek
- a prov:Agent;
- foaf:givenName "Derek"^^xsd:string;
- foaf:mbox <mailto:derek@example.org>;
- prov:actedOnBehalfOf :national_newspaper_inc;
-.
-
-:national_newspaper_inc
- a prov:Agent, prov:Organization;
- foaf:name "National Newspaper, Inc.";
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>An object property to express the accountability of an agent towards another agent. The subordinate agent acted on behalf of the responsible agent in an actual activity. </p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Delegation" href="#Delegation" class="owlclass">prov:Delegation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation" class="owlproperty">prov:qualifiedDelegation</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-delegation">delegation</a> </dd>
-
- </dl>
- </div>
- </div>
-
-</div>
-
- </div>
-
- <div id="cross-reference-expanded-terms" class="section">
- <h3><span class="secno">4.2 </span>Expanded Terms</h3>
- <p>The additional terms used to describe relations among Starting Point classes are discussed in <a href="#description-expanded-terms">Section 3.2</a>.</p>
-
-<div class="prov-expanded owl-classes at-a-glance">
- <ul class="hlist">
- <li>
- <a href="#Collection">prov:Collection</a>
- </li>
- <li>
- <a href="#EmptyCollection">prov:EmptyCollection</a>
- </li>
- <li>
- <a href="#Bundle">prov:Bundle</a>
- </li>
- <li>
- <a href="#Person">prov:Person</a>
- </li>
- <li>
- <a href="#SoftwareAgent">prov:SoftwareAgent</a>
- </li>
- <li>
- <a href="#Organization">prov:Organization</a>
- </li>
- <li>
- <a href="#Location">prov:Location</a>
- </li>
- </ul>
-</div>
-
-<div class="prov-expanded owl-properties at-a-glance">
- <ul class="hlist">
- <li class="object-property">
- <a href="#alternateOf">prov:alternateOf</a>
- </li>
- <li class="object-property">
- <a href="#specializationOf">prov:specializationOf</a>
- </li>
- <li class="datatype-property">
- <a href="#generatedAtTime">prov:generatedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#hadPrimarySource">prov:hadPrimarySource</a>
- </li>
- <li class="datatype-property">
- <a href="#value">prov:value</a>
- </li>
- <li class="object-property">
- <a href="#wasQuotedFrom">prov:wasQuotedFrom</a>
- </li>
- <li class="object-property">
- <a href="#wasRevisionOf">prov:wasRevisionOf</a>
- </li>
- <li class="datatype-property">
- <a href="#invalidatedAtTime">prov:invalidatedAtTime</a>
- </li>
- <li class="object-property">
- <a href="#wasInvalidatedBy">prov:wasInvalidatedBy</a>
- </li>
- <li class="object-property">
- <a href="#hadMember">prov:hadMember</a>
- </li>
- <li class="object-property">
- <a href="#wasStartedBy">prov:wasStartedBy</a>
- </li>
- <li class="object-property">
- <a href="#wasEndedBy">prov:wasEndedBy</a>
- </li>
- <li class="object-property">
- <a href="#invalidated">prov:invalidated</a>
- </li>
- <li class="object-property">
- <a href="#influenced">prov:influenced</a>
- </li>
- <li class="object-property">
- <a href="#atLocation">prov:atLocation</a>
- </li>
- <li class="object-property">
- <a href="#generated">prov:generated</a>
- </li>
- </ul>
-</div>
-
- <div class="prov-expanded owl-classes crossreference" >
-
- <div id="Collection" class="entity">
- <h3 id="x13--------class--prov-collection-----------------back-to-expanded-classes">
- <span class="xref" id="eg13">(13)</span>
- Class: <a href="#Collection"><span class="dotted" title="http://www.w3.org/ns/prov#Collection">prov:Collection</span></a>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Collection</p>
- <div class="definition"><p>A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix dcterms: <http://purl.org/dc/terms/> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/ontology#> .
-@prefix : <http://example.com/> .
-
-:todays-us-supreme-court
- a prov:Collection, :RobertsCourt;
-
- prov:qualifiedGeneration [
- a prov:Generation;
-
- # The generation is being qualified to be imprecise;
- # prov:generatedAtTime and prov:atTime specify exact instants in time.
- dcterms:date "2012"^^xsd:gYear;
- ];
-
- prov:hadMember
- <http://dbpedia.org/resource/John_Glover_Roberts,_Jr.>,
- <http://dbpedia.org/resource/Antonin_Scalia>,
- <http://dbpedia.org/resource/Anthony_Kennedy>,
- <http://dbpedia.org/resource/Clarence_Thomas>,
- <http://dbpedia.org/resource/Ruth_Bader_Ginsburg>,
- <http://dbpedia.org/resource/Stephen_Breyer>,
- <http://dbpedia.org/resource/Samuel_Alito>,
- <http://dbpedia.org/resource/Sonia_Sotomayor>,
- <http://dbpedia.org/resource/Elena_Kagan>;
-
- prov:wasDerivedFrom :the-first-us-supreme-court;
-
- dcterms:description :copied-string;
-.
-
-:copied-string
- a prov:Entity;
- prov:value """2010–present: A. Scalia A. Kennedy C. Thomas R.B. Ginsburg
- S. Breyer S. Alito S. Sotomayor E. Kagan""";
- prov:wasQuotedFrom :page-by-composition;
-.
-
-:page-by-seat
- a prov:Entity, ex:WikipediaPage;
- prov:specializationOf <http://purl.org/twc/page/wikipedia/us-supreme-court-by-seat>;
- prov:generatedAtTime "2011-08-31T12:51:00"^^xsd:dateTime;
-.
-
-:page-by-composition
- a prov:Entity, ex:WikipediaPage;
- prov:specializationOf <http://purl.org/twc/page/wikipedia/us-supreme-court-by-composition>;
- prov:generatedAtTime "2012-05-16T14:33:00"^^xsd:dateTime;
-.
-</pre>
- </div>
-
- <dl class="description">
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadMember" href="#hadMember">prov:hadMember</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>has subclass</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#EmptyCollection" href="#EmptyCollection" class="owlclass">prov:EmptyCollection</a>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-collection">collection</a> </dd>
- </dl>
- </div>
-
- <div id="EmptyCollection" class="entity">
- <h3 id="x14--------class--prov-emptycollection-----------------back-to-expanded-classes">
- <span class="xref" id="eg14">(14)</span>
- Class: <a href="#EmptyCollection"><span class="dotted" title="http://www.w3.org/ns/prov#EmptyCollection">prov:EmptyCollection</span></a>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#EmptyCollection</p>
- <div class="definition"><p>An empty collection is a collection without members.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.org/> .
-
-:c a prov:EmptyCollection . # The collection is believed to not contain members.
-</pre>
- </div>
-
- <dl class="description">
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Collection" href="#Collection" class="owlclass">prov:Collection</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadMember" href="#hadMember">prov:hadMember</a> <sup class="type-op" title="object property">op</sup> </dd>
- </dl>
- </div>
-
- <div id="Bundle" class="entity">
- <h3 id="x15--------class--prov-bundle-----------------back-to-expanded-classes">
- <span class="xref" id="eg15">(15)</span>
- Class: <a href="#Bundle"><span class="dotted" title="http://www.w3.org/ns/prov#Bundle">prov:Bundle</span></a>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Bundle</p>
- <div class="definition"><p>A bundle is a named set of provenance descriptions, and is itself an Entity, so allowing provenance of provenance to be expressed.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix my: <http://example.com/my#> .
-@prefix : <http://example.com/#> .
-@base <http://www.example.com/example.ttl> .
-
-<> # A provenance file located at http://www.example.com/example.ttl
- a prov:Bundle;
- prov:generatedAtTime "2012-05-24T09:30:00"^^xsd:dateTime;
- prov:wasAttributedTo :bob;
-.
-
-:report1
- a my:Report, prov:Entity;
- my:version "1";
- prov:generatedAtTime "2012-05-24T01:00:00"^^xsd:dateTime;
- prov:wasAttributedTo :bob;
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>Note that there are kinds of bundles (e.g. handwritten letters, audio recordings, etc.) that are not expressed in PROV-O, but can be still be described by PROV-O.</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-bundle-entity">bundle-entity</a> </dd>
- </dl>
- </div>
-
- <div id="Person" class="entity">
- <h3 id="x16--------class--prov-person-----------------back-to-expanded-classes">
- <span class="xref" id="eg16">(16)</span>
- Class: <a href="#Person"><span class="dotted" title="http://www.w3.org/ns/prov#Person">prov:Person</span></a>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Person</p>
- <div class="definition"><p>Agents of type Person are people.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix : <http://example.com/> .
-
-<http://dbpedia.org/resource/Pablo_Picasso>
- a prov:Person, prov:Agent;
- foaf:depiction <http://upload.wikimedia.org/wikipedia/commons/9/98/Pablo_picasso_1.jpg>;
-.
-</pre>
- </div>
-
- <dl class="description">
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation">prov:qualifiedDelegation</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf">prov:actedOnBehalfOf</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-agent">agent</a> </dd>
- </dl>
- </div>
-
- <div id="SoftwareAgent" class="entity">
- <h3 id="x17--------class--prov-softwareagent-----------------back-to-expanded-classes">
- <span class="xref" id="eg17">(17)</span>
- Class: <a href="#SoftwareAgent"><span class="dotted" title="http://www.w3.org/ns/prov#SoftwareAgent">prov:SoftwareAgent</span></a>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#SoftwareAgent</p>
- <div class="definition"><p>A software agent is running software.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-# Googlebot is Google's web crawling bot;
-# it can initiate and participate in web-crawling activities.
-
-:googlebot
- a prov:SoftwareAgent;
- rdfs:label "Googlebot"^^xsd:string;
-.
-</pre>
- </div>
-
- <dl class="description">
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation">prov:qualifiedDelegation</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf">prov:actedOnBehalfOf</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-agent">agent</a> </dd>
- </dl>
- </div>
-
- <div id="Organization" class="entity">
- <h3 id="x18--------class--prov-organization-----------------back-to-expanded-classes">
- <span class="xref" id="eg18">(18)</span>
- Class: <a href="#Organization"><span class="dotted" title="http://www.w3.org/ns/prov#Organization">prov:Organization</span></a>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Organization</p>
- <div class="definition"><p>Agents of type Organization are social institutions such as companies, societies etc.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix : <http://example.com/> .
-
-:<acronym title="World Wide Web Consortium">W3C</acronym>
- a prov:Agent, prov:Organization;
- foaf:name "World Wide Web Consortium";
-.
-</pre>
- </div>
-
- <dl class="description">
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation">prov:qualifiedDelegation</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf">prov:actedOnBehalfOf</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-agent">agent</a> </dd>
- </dl>
- </div>
-
- <div id="Location" class="entity">
- <h3 id="x19--------class--prov-location-----------------back-to-expanded-classes">
- <span class="xref" id="eg19">(19)</span>
- Class: <a href="#Location"><span class="dotted" title="http://www.w3.org/ns/prov#Location">prov:Location</span></a>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Location</p>
- <div class="definition"><p>A location can be an identifiable geographic place (ISO 19112), but it can also be a non-geographic place such as a directory, row, or column. As such, there are numerous ways in which location can be expressed, such as by a coordinate, address, landmark, and so forth.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix sioc: <http://rdfs.org/sioc/ns#> .
-@prefix : <http://example.com/> .
-
-# A Location can be a path or a geographical location.
-
-:post9821
- a prov:Entity, sioc:Post;
- prov:wasGeneratedBy :publicationActivity1123;
- prov:atLocation :more-crime-happens-in-cities;
- prov:qualifiedGeneration [
- a prov:Generation;
- prov:activity :publicationActivity1123;
- prov:atTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:atLocation <http://dbpedia.org/resource/Madrid>;
- ];
-.
-
-:publicationActivity1123 a prov:Activity.
-:more-crime-happens-in-cities a prov:Location.
-<http://dbpedia.org/resource/Madrid> a prov:Location.
-</pre>
- </div>
-
- <dl class="description">
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#atLocation" href="#atLocation">prov:atLocation</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribute-location">attribute-location</a> </dd>
- </dl>
- </div>
-</div>
-<div class="prov-expanded owl-properties crossreference" >
- <div id="alternateOf" class="entity">
- <h3 id="x20--------property--prov-alternateof-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg20">(20)</span>
- Property: <a href="#alternateOf"><span class="dotted" title="http://www.w3.org/ns/prov#alternateOf">prov:alternateOf</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#alternateOf</p>
- <div class="definition def-from-1"><p>Two alternate entities present aspects of the same thing. These aspects may be the same or different, and the alternate entities may or may not overlap in time.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:bbc a prov:Agent .
-
-:london_forecast_0412
- a prov:Entity;
- prov:wasAttributedTo :bbc;
- prov:wasGeneratedBy [
- a prov:Activity;
- prov:endedAtTime "2012-04-12T00:00:00-04:00"^^xsd:dateTime;
- ];
- prov:alternateOf :london_forecast_0413;
-.
-
-:london_forecast_0413
- a prov:Entity;
- prov:wasAttributedTo :bbc;
- prov:wasGeneratedBy [
- a prov:Activity;
- prov:endedAtTime "2012-04-13T00:00:00-04:00"^^xsd:dateTime;
- ];
- prov:alternateOf :london_forecast_0412;
-.
-
-## :london_forecast_0412 and :london_forecast_0413 are both
-## specialization of the more general entity :london_forecast
-
-:london_forecast
- a prov:Entity;
- prov:wasAttributedTo :bbc;
-.
-
-:london_forecast_0412
- prov:specializationOf :london_forecast;
-.
-:london_forecast_0413
- prov:specializationOf :london_forecast;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has sub-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#specializationOf" href="#specializationOf" class="owlclass">prov:specializationOf</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-alternate">alternate</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="specializationOf" class="entity">
- <h3 id="x21--------property--prov-specializationof-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg21">(21)</span>
- Property: <a href="#specializationOf"><span class="dotted" title="http://www.w3.org/ns/prov#specializationOf">prov:specializationOf</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#specializationOf</p>
- <div class="definition def-from-1"><p>An entity that is a specialization of another shares all aspects of the latter, and additionally presents more specific aspects of the same thing as the latter. In particular, the lifetime of the entity being specialized contains that of any specialization. Examples of aspects include a time period, an abstraction, and a context associated with the entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:london_forecast_0412
- a prov:Entity;
- prov:wasAttributedTo :bbc;
- prov:wasGeneratedBy [
- a prov:Activity;
- prov:endedAtTime "2012-04-12T00:00:00-04:00"^^xsd:dateTime;
- ];
-.
-
-:london_forecast_0413
- a prov:Entity;
- prov:wasAttributedTo :bbc;
- prov:wasGeneratedBy [
- a prov:Activity;
- prov:endedAtTime "2012-04-13T00:00:00-04:00"^^xsd:dateTime;
- ];
-.
-
-:london_forecast
- a prov:Entity;
- prov:wasAttributedTo :bbc;
-.
-
-## :london_forecast_0412 and :london_forecast_0413 are both
-## specialization of the more general entity :london_forecast
-
-:london_forecast_0412
- prov:alternateOf :london_forecast_0413;
- prov:specializationOf :london_forecast;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#alternateOf" href="#alternateOf" class="owlclass">prov:alternateOf</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-specialization">specialization</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="generatedAtTime" class="entity">
- <h3 id="x22--------property--prov-generatedattime-dp-----------------back-to-expanded-properties">
- <span class="xref" id="eg22">(22)</span>
- Property: <a href="#generatedAtTime"><span class="dotted" title="http://www.w3.org/ns/prov#generatedAtTime">prov:generatedAtTime</span></a> <sup class="type-dp" title="data property">dp</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#generatedAtTime</p>
- <div class="definition def-from-5"><p>Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-# A widget was generated 1:35:23 PM on April 3, 2012 UTC
-
-:widget-789532
- a prov:Entity;
- prov:generatedAtTime "2012-04-03T13:35:23Z"^^xsd:dateTime;
-.
-
-# The above statement is equivalent to:
-# :widget-789532 prov:qualifiedGeneration [ prov:atTime "2012-04-03T13:35:23Z"^^xsd:dateTime ] .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The time at which an entity was completely created and is available for use.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- http://www.w3.org/2001/XMLSchema#dateTime
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlclass">prov:Generation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime" class="owlproperty">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Generation">Generation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="hadPrimarySource" class="entity">
- <h3 id="x23--------property--prov-hadprimarysource-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg23">(23)</span>
- Property: <a href="#hadPrimarySource"><span class="dotted" title="http://www.w3.org/ns/prov#hadPrimarySource">prov:hadPrimarySource</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#hadPrimarySource</p>
- <div class="definition def-from-5"><p>A primary source for a topic refers to something produced by some agent with direct experience and knowledge about the topic, at the time of the topic's study, without benefit from hindsight.
-
-Because of the directness of primary sources, they 'speak for themselves' in ways that cannot be captured through the filter of secondary sources. As such, it is important for secondary sources to reference those primary sources from which they were derived, so that their reliability can be investigated.
-
-A primary source relation is a particular case of derivation of secondary materials from their primary sources. It is recognized that the determination of primary sources can be up to interpretation, and should be done according to conventions accepted within the application's domain.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix lang: <http://lexvo.org/id/iso639-3/> .
-@prefix dcterms: <http://purl.org/dc/terms/> .
-@prefix frbr: <http://purl.org/vocab/frbr/core#> .
-@prefix : <http://example.com/> .
-
-## Having an primary source is a particular case of derivation.
-
-<http://www.gutenberg.org/ebooks/996>
- a prov:Entity, frbr:Work;
- dcterms:title "Don Quixote";
- prov:wasAttributedTo :ormsby;
- dcterms:language lang:eng;
- prov:hadPrimarySource <http://cultura.linkeddata.es/BNE/resource/C1001/XX2197892>;
-.
-
-#### The English version book is a translation that is based on the original Spanish book
-
-<http://cultura.linkeddata.es/BNE/resource/C1001/XX2197892>
- a prov:Entity, frbr:Work;
- prov:wasAttributedTo :cervantes;
- dcterms:language lang:spa;
-.
-
-:cervantes
- a prov:Person;
- foaf:name "Miguel de Cervantes";
-.
-
-:ormsby
- a prov:Person;
- foaf:name "John Ormsby";
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlclass">prov:wasDerivedFrom</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedPrimarySource" href="#qualifiedPrimarySource" class="owlproperty">prov:qualifiedPrimarySource</a> <sup class="type-op" title="object property">op</sup>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#PrimarySource" href="#PrimarySource" class="owlclass">prov:PrimarySource</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-primary-source">primary-source</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="value" class="entity">
- <h3 id="x24--------property--prov-value-dp-----------------back-to-expanded-properties">
- <span class="xref" id="eg24">(24)</span>
- Property: <a href="#value"><span class="dotted" title="http://www.w3.org/ns/prov#value">prov:value</span></a> <sup class="type-dp" title="data property">dp</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#value</p>
- <div class="definition def-from-1"><p>Provides a value that is a direct representation of an entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:copied-string
- a prov:Entity;
- prov:value
- """2010–present: A. Scalia A. Kennedy C. Thomas R.B. Ginsburg
- S. Breyer S. Alito S. Sotomayor E. Kagan""";
- prov:wasQuotedFrom
- <http://purl.org/twc/page/wikipedia/us-supreme-court-by-composition>;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribute-value">attribute-value</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasQuotedFrom" class="entity">
- <h3 id="x25--------property--prov-wasquotedfrom-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg25">(25)</span>
- Property: <a href="#wasQuotedFrom"><span class="dotted" title="http://www.w3.org/ns/prov#wasQuotedFrom">prov:wasQuotedFrom</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasQuotedFrom</p>
- <div class="definition def-from-5"><p>A quotation is the repeat of (some or all of) an entity, such as text or image, by someone who may or may not be its original author. Quotation is a particular case of derivation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:bl-dagstuhl
- a prov:Entity;
-
- prov:value """During the workshop, it became clear to me that the consensus
- based models (which are often graphical in nature) can not only be
- formalized but also be directly connected to these database focused
- formalizations. I just needed to get over the differences in syntax.
- This could imply that we could have nice way to trace provenance across
- systems and through databases and be able to understand the
- mathematical properties of this interconnection.""";
-
- prov:wasQuotedFrom <http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>;
-.
-
-<http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>
- a prov:Entity;
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>An entity is derived from an original entity by copying, or 'quoting', some or all of it.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlclass">prov:wasDerivedFrom</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedQuotation" href="#qualifiedQuotation" class="owlproperty">prov:qualifiedQuotation</a> <sup class="type-op" title="object property">op</sup>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#Quotation" href="#Quotation" class="owlclass">prov:Quotation</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-quotation">quotation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasRevisionOf" class="entity">
- <h3 id="x26--------property--prov-wasrevisionof-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg26">(26)</span>
- Property: <a href="#wasRevisionOf"><span class="dotted" title="http://www.w3.org/ns/prov#wasRevisionOf">prov:wasRevisionOf</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasRevisionOf</p>
- <div class="definition def-from-5"><p>A revision is a derivation for which the resulting entity is a revised version of some original. The implication here is that the resulting entity contains substantial content from the original. Revision is a particular case of derivation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix sioc: <http://rdfs.org/sioc/ns#> .
-@prefix : <http://example.com/> .
-
-:post9821v1
- a prov:Entity, sioc:Post;
- prov:wasRevisionOf :post9821;
- rdfs:comment ":post9821v1 is a post, which is a revision of the original post :post9821.";
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>A revision is a derivation that revises an entity into a revised version.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlclass">prov:wasDerivedFrom</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Revision" href="#Revision" class="owlclass">prov:Revision</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedRevision" href="#qualifiedRevision" class="owlproperty">prov:qualifiedRevision</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-revision">revision</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="invalidatedAtTime" class="entity">
- <h3 id="x27--------property--prov-invalidatedattime-dp-----------------back-to-expanded-properties">
- <span class="xref" id="eg27">(27)</span>
- Property: <a href="#invalidatedAtTime"><span class="dotted" title="http://www.w3.org/ns/prov#invalidatedAtTime">prov:invalidatedAtTime</span></a> <sup class="type-dp" title="data property">dp</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#invalidatedAtTime</p>
- <div class="definition def-from-5"><p>Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/ontology#> .
-@prefix : <http://example.com/> .
-
-:the-Painter
- a prov:Entity, ex:Painting;
- rdfs:label "Le Peintre"@fr, "The Painter"@en;
- prov:wasAttributedTo <http://dbpedia.org/resource/Pablo_Picasso>;
- prov:invalidatedAtTime "1998-09-02T01:31:00Z"^^xsd:dateTime;
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The time at which an entity was invalidated (i.e., no longer usable).</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- http://www.w3.org/2001/XMLSchema#dateTime
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Invalidation" href="#Invalidation" class="owlclass">prov:Invalidation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime" class="owlproperty">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Invalidation">Invalidation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasInvalidatedBy" class="entity">
- <h3 id="x28--------property--prov-wasinvalidatedby-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg28">(28)</span>
- Property: <a href="#wasInvalidatedBy"><span class="dotted" title="http://www.w3.org/ns/prov#wasInvalidatedBy">prov:wasInvalidatedBy</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasInvalidatedBy</p>
- <div class="definition def-from-5"><p>Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix : <http://example.com/> .
-
-:the-Painter
- a prov:Entity, :Painting;
- rdfs:label "Le Peintre"@fr, "The Painter"@en;
- prov:wasAttributedTo <http://dbpedia.org/resource/Pablo_Picasso>;
- prov:wasInvalidatedBy :Swissair_Flight_111_crash; #The painting was destroyed in an airplane crash
-.
-
-<http://dbpedia.org/resource/Pablo_Picasso>
- a prov:Agent;
- foaf:depiction <http://upload.wikimedia.org/wikipedia/commons/9/98/Pablo_picasso_1.jpg>;
-.
-
-:Swissair_Flight_111_crash
- a prov:Activity;
- prov:used <http://dbpedia.org/resource/Swissair_Flight_111>;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Invalidation" href="#Invalidation" class="owlclass">prov:Invalidation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInvalidation" href="#qualifiedInvalidation" class="owlproperty">prov:qualifiedInvalidation</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Invalidation">Invalidation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="hadMember" class="entity">
- <h3 id="x29--------property--prov-hadmember-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg29">(29)</span>
- Property: <a href="#hadMember"><span class="dotted" title="http://www.w3.org/ns/prov#hadMember">prov:hadMember</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#hadMember</p>
- <div class="definition def-from-2"><p>A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix dcterms: <http://purl.org/dc/terms/> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/ontology#> .
-@prefix : <http://example.com/> .
-
-:todays-us-supreme-court
- a prov:Collection, ex:RobertsCourt;
- dcterms:description [
- a prov:Entity;
- prov:value """2010–present: A. Scalia A. Kennedy C. Thomas R.B. Ginsburg S.
- Breyer S. Alito S. Sotomayor E. Kagan""";
- prov:wasQuotedFrom :page-by-composition;
- ];
- prov:qualifiedGeneration [
- a prov:Generation;
-
- # Since we need to be imprecise, we can't use prov:generatedAtTime or prov:atTime
- dcterms:date "2012"^^xsd:gYear;
- ];
-
- prov:wasDerivedFrom :the-first-us-supreme-court;
-
- prov:hadMember
- <http://dbpedia.org/resource/John_Glover_Roberts,_Jr.>,
- <http://dbpedia.org/resource/Antonin_Scalia>,
- <http://dbpedia.org/resource/Anthony_Kennedy>,
- <http://dbpedia.org/resource/Clarence_Thomas>,
- <http://dbpedia.org/resource/Ruth_Bader_Ginsburg>,
- <http://dbpedia.org/resource/Stephen_Breyer>,
- <http://dbpedia.org/resource/Samuel_Alito>,
- <http://dbpedia.org/resource/Sonia_Sotomayor>,
- <http://dbpedia.org/resource/Elena_Kagan>;
-.
-
-:page-by-seat
- a prov:Entity, ex:WikipediaPage;
- prov:specializationOf <http://purl.org/twc/page/wikipedia/us-supreme-court-by-seat>;
- prov:generatedAtTime "2011-08-31T12:51:00"^^xsd:dateTime;
-.
-
-:page-by-composition
- a prov:Entity, ex:WikipediaPage;
- prov:specializationOf <http://purl.org/twc/page/wikipedia/us-supreme-court-by-composition>;
- prov:generatedAtTime "2012-05-16T14:33:00"^^xsd:dateTime;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Collection" href="#Collection" class="owlclass">prov:Collection</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-collection">collection</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasStartedBy" class="entity">
- <h3 id="x30--------property--prov-wasstartedby-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg30">(30)</span>
- Property: <a href="#wasStartedBy"><span class="dotted" title="http://www.w3.org/ns/prov#wasStartedBy">prov:wasStartedBy</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasStartedBy</p>
- <div class="definition def-from-5"><p>Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-# Use prov:qualifiedStart to see when and where the activity was started
-
-:experiment
- a prov:Activity;
- prov:wasStartedBy :researcher;
-.
-
-:researcher a prov:Agent .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>Start is when an activity is deemed to have started. A start may refer to an entity, known as trigger, that initiated the activity.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlclass">prov:Start</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedStart" href="#qualifiedStart" class="owlproperty">prov:qualifiedStart</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Start">Start</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="wasEndedBy" class="entity">
- <h3 id="x31--------property--prov-wasendedby-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg31">(31)</span>
- Property: <a href="#wasEndedBy"><span class="dotted" title="http://www.w3.org/ns/prov#wasEndedBy">prov:wasEndedBy</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasEndedBy</p>
- <div class="definition def-from-5"><p>End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:experiment
- a prov:Activity;
- prov:wasEndedBy :inconsistentResult;
- prov:qualifiedEnd [
- a prov:End;
- prov:entity :inconsistentResult;
- prov:atTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:atLocation :scienceLab_003;
- ];
-.
-
-:inconsistentResult a prov:Entity .
-:scienceLab_003 a prov:Location .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>End is when an activity is deemed to have ended. An end may refer to an entity, known as trigger, that terminated the activity.</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#End" href="#End" class="owlclass">prov:End</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedEnd" href="#qualifiedEnd" class="owlproperty">prov:qualifiedEnd</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-End">End</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="invalidated" class="entity">
- <h3 id="x32--------property--prov-invalidated-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg32">(32)</span>
- Property: <a href="#invalidated"><span class="dotted" title="http://www.w3.org/ns/prov#invalidated">prov:invalidated</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#invalidated</p>
- <div class="definition def-from-2"><p>Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix ex: <http://example.com/ontology#> .
-@prefix : <http://example.com/> .
-
-:swissair_Flight_111_crash
- a prov:Activity;
- prov:used <http://dbpedia.org/resource/Swissair_Flight_111>;
- prov:invalidated :the-Painter;
-.
-
-:the-Painter
- a prov:Entity, ex:Painting;
- rdfs:label "Le Peintre"@fr, "The Painter"@en;
- prov:wasAttributedTo <http://dbpedia.org/resource/Pablo_Picasso>;
-
- # Inferred from prov:invalidated
- prov:wasInvalidatedBy :swissair_Flight_111_crash;
-.
-
-<http://dbpedia.org/resource/Pablo_Picasso>
- a prov:Agent;
- foaf:depiction <http://upload.wikimedia.org/wikipedia/commons/9/98/Pablo_picasso_1.jpg>;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#influenced" href="#influenced" class="owlclass">prov:influenced</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has inverse</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy" class="owlclass">prov:wasInvalidatedBy</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Invalidation">Invalidation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="influenced" class="entity">
- <h3 id="x33--------property--prov-influenced-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg33">(33)</span>
- Property: <a href="#influenced"><span class="dotted" title="http://www.w3.org/ns/prov#influenced">prov:influenced</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#influenced</p>
- <div class="definition def-from-2"><p>Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix w3: <http://example.com/w3/> .
-@prefix tr: <http://example.com/tech-report/> .
-@prefix : <http://example.com/> .
-
-# prov:influenced is a top-level property that links any
-# Entity, Activity, or Agent to any other
-# Entity, Activity, or Agent that it had an effect upon.
-
-w3:Consortium
- a prov:Agent;
- prov:influenced tr:WD-prov-dm-20111215;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has inverse</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlclass">prov:wasInfluencedBy</a>
- </li>
- </ul>
- </dd>
-
- <dt>has sub-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#generated" href="#generated" class="owlclass">prov:generated</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#invalidated" href="#invalidated" class="owlclass">prov:invalidated</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-influence">influence</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="atLocation" class="entity">
- <h3 id="x34--------property--prov-atlocation-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg34">(34)</span>
- Property: <a href="#atLocation"><span class="dotted" title="http://www.w3.org/ns/prov#atLocation">prov:atLocation</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#atLocation</p>
- <div class="definition def-from-2"><p>A location can be an identifiable geographic place (ISO 19112), but it can also be a non-geographic place such as a directory, row, or column. As such, there are numerous ways in which location can be expressed, such as by a coordinate, address, landmark, and so forth.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix sioc: <http://rdfs.org/sioc/ns#> .
-@prefix : <http://example.com/> .
-
-# A Location can be a path or a geographical location.
-
-:post9821
- a prov:Entity, sioc:Post;
- prov:wasGeneratedBy :publicationActivity1123;
- prov:atLocation :more-crime-happens-in-cities;
- prov:qualifiedGeneration [
- a prov:Generation;
- prov:activity :publicationActivity1123;
- prov:atTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:atLocation <http://dbpedia.org/resource/Madrid>;
- ];
-.
-
-:publicationActivity1123 a prov:Activity .
-:more-crime-happens-in-cities a prov:Location .
-<http://dbpedia.org/resource/Madrid> a prov:Location .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The Location of any resource.</p>
- </div>
- <div class="comment "><p>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- or <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- or <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- or <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Location" href="#Location" class="owlclass">prov:Location</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribute-location">attribute-location</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="generated" class="entity">
- <h3 id="x35--------property--prov-generated-op-----------------back-to-expanded-properties">
- <span class="xref" id="eg35">(35)</span>
- Property: <a href="#generated"><span class="dotted" title="http://www.w3.org/ns/prov#generated">prov:generated</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-expanded-owl-terms-at-a-glance">expanded properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#generated</p>
- <div class="definition def-from-2"><p>Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:proteinDigestion
- a prov:Activity;
- prov:generated :peptideSample1;
-.
-
-:peptideSample1 a prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#influenced" href="#influenced" class="owlclass">prov:influenced</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has inverse</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy" class="owlclass">prov:wasGeneratedBy</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Generation">Generation</a> </dd>
-
- </dl>
- </div>
- </div>
-
-</div>
-
- </div>
-
- <div id="cross-reference-qualified-terms" class="section">
- <h3><span class="secno">4.3 </span>Qualified Terms</h3>
- <p>The terms used to qualify the Starting Point and Expanded properties are discussed in <a href="#description-qualified-terms">Section 3.3</a>.</p>
-
-<div class="prov-qualified owl-classes at-a-glance">
- <ul class="hlist">
- <li>
- <a href="#Influence">prov:Influence</a>
- </li>
- <li>
- <a href="#EntityInfluence">prov:EntityInfluence</a>
- </li>
- <li>
- <a href="#Usage">prov:Usage</a>
- </li>
- <li>
- <a href="#Start">prov:Start</a>
- </li>
- <li>
- <a href="#End">prov:End</a>
- </li>
- <li>
- <a href="#Derivation">prov:Derivation</a>
- </li>
- <li>
- <a href="#PrimarySource">prov:PrimarySource</a>
- </li>
- <li>
- <a href="#Quotation">prov:Quotation</a>
- </li>
- <li>
- <a href="#Revision">prov:Revision</a>
- </li>
- <li>
- <a href="#ActivityInfluence">prov:ActivityInfluence</a>
- </li>
- <li>
- <a href="#Generation">prov:Generation</a>
- </li>
- <li>
- <a href="#Communication">prov:Communication</a>
- </li>
- <li>
- <a href="#Invalidation">prov:Invalidation</a>
- </li>
- <li>
- <a href="#AgentInfluence">prov:AgentInfluence</a>
- </li>
- <li>
- <a href="#Attribution">prov:Attribution</a>
- </li>
- <li>
- <a href="#Association">prov:Association</a>
- </li>
- <li>
- <a href="#Plan">prov:Plan</a>
- </li>
- <li>
- <a href="#Delegation">prov:Delegation</a>
- </li>
- <li>
- <a href="#InstantaneousEvent">prov:InstantaneousEvent</a>
- </li>
- <li>
- <a href="#Role">prov:Role</a>
- </li>
- </ul>
-</div>
-
-<div class="prov-qualified owl-properties at-a-glance">
- <ul class="hlist">
- <li class="object-property">
- <a href="#wasInfluencedBy">prov:wasInfluencedBy</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedInfluence">prov:qualifiedInfluence</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedGeneration">prov:qualifiedGeneration</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedDerivation">prov:qualifiedDerivation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedPrimarySource">prov:qualifiedPrimarySource</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedQuotation">prov:qualifiedQuotation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedRevision">prov:qualifiedRevision</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedAttribution">prov:qualifiedAttribution</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedInvalidation">prov:qualifiedInvalidation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedStart">prov:qualifiedStart</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedUsage">prov:qualifiedUsage</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedCommunication">prov:qualifiedCommunication</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedAssociation">prov:qualifiedAssociation</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedEnd">prov:qualifiedEnd</a>
- </li>
- <li class="object-property">
- <a href="#qualifiedDelegation">prov:qualifiedDelegation</a>
- </li>
- <li class="object-property">
- <a href="#influencer">prov:influencer</a>
- </li>
- <li class="object-property">
- <a href="#p_entity">prov:entity</a>
- </li>
- <li class="object-property">
- <a href="#hadUsage">prov:hadUsage</a>
- </li>
- <li class="object-property">
- <a href="#hadGeneration">prov:hadGeneration</a>
- </li>
- <li class="object-property">
- <a href="#p_activity">prov:activity</a>
- </li>
- <li class="object-property">
- <a href="#p_agent">prov:agent</a>
- </li>
- <li class="object-property">
- <a href="#hadPlan">prov:hadPlan</a>
- </li>
- <li class="object-property">
- <a href="#hadActivity">prov:hadActivity</a>
- </li>
- <li class="datatype-property">
- <a href="#atTime">prov:atTime</a>
- </li>
- <li class="object-property">
- <a href="#hadRole">prov:hadRole</a>
- </li>
- </ul>
-</div>
-
- <div class="prov-qualified owl-classes crossreference" >
-
- <div id="Influence" class="entity">
- <h3 id="x36--------class--prov-influence-----------------back-to-qualified-classes">
- <span class="xref" id="eg36">(36)</span>
- Class: <a href="#Influence"><span class="dotted" title="http://www.w3.org/ns/prov#Influence">prov:Influence</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Influence</p>
- <div class="definition"><p>Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix my: <http://example.com/ontology#> .
-@prefix : <http://example.com/> .
-
-# Although a domain extension (e.g. ':wasConductedBy') is not defined by PROV-O,
-# the relation between a surgery and an agent can still be qualified
-# by reusing prov:Influence and one of its three subclasses
-# (depending on the type of influencer):
-# AgentInfluence, EntityInfluence, and ActivityInfluence.
-
-my:wasConductedBy rdfs:subPropertyOf prov:wasAssociatedWith .
-
-:conductingSurgery_1
- a prov:Activity;
-
- # This unqualified influence is unknown in PROV,
- # but would be a subproperty of wasAssociatedWith.
- my:wasConductedBy :bob;
-
- # Even though PROV systems do not understand my:wasConductedBy,
- prov:qualifiedAssociation [
- # they can recognize that the unknown relation
- # is being qualified with a prov:hadRole.
- a prov:Association,
- prov:AgentInfluence, # Inferred
- prov:Influence; # Inferred
- prov:agent :bob; # The object of my:wasConductedBy
- prov:hadRole my:surgeon;
- ];
-.
-
-:bob a prov:Agent .
-my:surgeon a prov:Role .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>Because prov:Influence is a broad relation, its most specific subclasses (e.g. prov:Communication, prov:Delegation, prov:End, prov:Revision, etc.) should be used when applicable.</p>
- </dd>
- <dd class="comment"><p>An instance of prov:Influence provides additional descriptions about the binary prov:wasInfluencedBy relation from some influenced Activity, Entity, or Agent to the influencing Activity, Entity, or Agent. For example, :stomach_ache prov:wasInfluencedBy :spoon; prov:qualifiedInfluence [ a prov:Influence; prov:entity :spoon; :foo :bar ] . Because prov:Influence is a broad relation, the more specific relations (Communication, Delegation, End, etc.) should be used when applicable.</p>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#influencer" href="#influencer">prov:influencer</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole">prov:hadRole</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#ActivityInfluence" href="#ActivityInfluence" class="owlclass">prov:ActivityInfluence</a>
- , <a title="http://www.w3.org/ns/prov#AgentInfluence" href="#AgentInfluence" class="owlclass">prov:AgentInfluence</a>
- , <a title="http://www.w3.org/ns/prov#EntityInfluence" href="#EntityInfluence" class="owlclass">prov:EntityInfluence</a>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlproperty">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-influence">influence</a> </dd>
- </dl>
- </div>
-
- <div id="EntityInfluence" class="entity">
- <h3 id="x37--------class--prov-entityinfluence-----------------back-to-qualified-classes">
- <span class="xref" id="eg37">(37)</span>
- Class: <a href="#EntityInfluence"><span class="dotted" title="http://www.w3.org/ns/prov#EntityInfluence">prov:EntityInfluence</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#EntityInfluence</p>
- <div class="editors definition"><p>EntityInfluence is the capacity of an entity to have an effect on the character, development, or behavior of another by means of usage, start, end, derivation, or other. </p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:sortActivity
- a prov:Activity;
- prov:used :rawData;
- prov:qualifiedUsage [
- a prov:Usage,
- prov:EntityInfluence; ## Instances of Start, End, Usage, Derivation, and Invalidation
- prov:entity :datasetA; ## qualify the influenced of an Entity (cited by prov:entity).
- prov:hadRole :inputToBeSorted;
- ];
- prov:generated :sortedData;
-.
-
-:rawData a prov:Entity .
-:sortedData a prov:Entity .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>EntityInfluence provides additional descriptions of an Entity's binary influence upon any other kind of resource. Instances of EntityInfluence use the prov:entity property to cite the influencing Entity.</p>
- </dd>
- <dd class="comment"><p>It is not recommended that the type EntityInfluence be asserted without also asserting one of its more specific subclasses.</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#entity" href="#p_entity">prov:entity</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole">prov:hadRole</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#influencer" href="#influencer">prov:influencer</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#End" href="#End" class="owlclass">prov:End</a>
- , <a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlclass">prov:Start</a>
- , <a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlclass">prov:Usage</a>
- , <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </dd>
- </dl>
- </div>
-
- <div id="Usage" class="entity">
- <h3 id="x38--------class--prov-usage-----------------back-to-qualified-classes">
- <span class="xref" id="eg38">(38)</span>
- Class: <a href="#Usage"><span class="dotted" title="http://www.w3.org/ns/prov#Usage">prov:Usage</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Usage</p>
- <div class="definition"><p>Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:sortActivity
- a prov:Activity;
- prov:startedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:qualifiedUsage [
- a prov:Usage;
- prov:entity :datasetA; ## The entity used by the prov:Usage
- prov:hadRole :inputToBeSorted; ## the role of the entity in this prov:Usage
- ];
- prov:generated :datasetB;
-.
-
-:datasetA a prov:Entity .
-:datasetB a prov:Entity .
-:inputToBeSorted a prov:Role .
-
-## The role of :datasetA cannot be expressed using only starting-point terms:
-
-:sortActivity
- a prov:Activity;
- prov:startedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:used :datasetA;
- prov:generated :datasetB;
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Usage provides additional descriptions about the binary prov:used relation from some prov:Activity to an prov:Entity that it used. For example, :keynote prov:used :podium; prov:qualifiedUsage [ a prov:Usage; prov:entity :podium; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- , <a title="http://www.w3.org/ns/prov#EntityInfluence" href="#EntityInfluence" class="owlclass">prov:EntityInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup> , <a title="http://www.w3.org/ns/prov#entity" href="#p_entity">prov:entity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadUsage" href="#hadUsage">prov:hadUsage</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#qualifiedUsage" href="#qualifiedUsage">prov:qualifiedUsage</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#used" href="#used" class="owlproperty">prov:used</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Usage">Usage</a> </dd>
- </dl>
- </div>
-
- <div id="Start" class="entity">
- <h3 id="x39--------class--prov-start-----------------back-to-qualified-classes">
- <span class="xref" id="eg39">(39)</span>
- Class: <a href="#Start"><span class="dotted" title="http://www.w3.org/ns/prov#Start">prov:Start</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Start</p>
- <div class="definition"><p>Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-### Start can be used to qualify wasStartedBy with time and location information.
-### In this example, a consistency checking activity is started by the update of a data record.
-
-:consistency_checking
- a prov:Activity;
- prov:wasStartedBy :updated_data_record;
- prov:qualifiedStart [
- a prov:Start;
- prov:entity :updated_data_record;
- prov:atTime "2011-07-06T01:48:36Z"^^xsd:dateTime;
- prov:atLocation :scienceLab_003;
- prov:hadActivity :syntax_checking;
- ];
-.
-
-:updated_data_record a prov:Entity .
-
-### There is an explicit process of checking the syntax of the updated data record
-
-:syntax_checking
- a prov:Activity ;
- prov:startedAtTime "2011-07-06T01:48:36Z"^^xsd:dateTime;
- prov:endedAtTime "2011-07-06T02:12:36Z"^^xsd:dateTime;
- prov:wasAssociatedWith :syntax_checker ;
-.
-
-:syntax_checker a prov:SoftwareAgent .</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Start provides additional descriptions about the binary prov:wasStartedBy relation from some started prov:Activity to an prov:Entity that started it. For example, :foot_race prov:wasStartedBy :bang; prov:qualifiedStart [ a prov:Start; prov:entity :bang; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ] .</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- , <a title="http://www.w3.org/ns/prov#EntityInfluence" href="#EntityInfluence" class="owlclass">prov:EntityInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup> , <a title="http://www.w3.org/ns/prov#entity" href="#p_entity">prov:entity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedStart" href="#qualifiedStart">prov:qualifiedStart</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasStartedBy" href="#wasStartedBy" class="owlproperty">prov:wasStartedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Start">Start</a> </dd>
- </dl>
- </div>
-
- <div id="End" class="entity">
- <h3 id="x40--------class--prov-end-----------------back-to-qualified-classes">
- <span class="xref" id="eg40">(40)</span>
- Class: <a href="#End"><span class="dotted" title="http://www.w3.org/ns/prov#End">prov:End</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#End</p>
- <div class="definition"><p>End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-### End can be used to qualify wasEndedBy with time and location information.
-### In this example, an experiment is stopped because an intermediate inconsitent resul.
-
-:experiment
- a prov:Activity;
- prov:wasEndedBy :inconsistentResult;
- prov:qualifiedEnd [
- a prov:End;
- prov:entity :inconsistentResult;
- prov:atTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:atLocation :scienceLab_003;
- prov:hadActivity :analyse_intermediate_result ;
- ];
-.
-
-:inconsistentResult a prov:Entity .
-
-### An implicit process analyzes the intermediate result to confirm its expected consistency
-
-analyse_intermediate_result
- a prov:Activity ;
- prov:startedAtTime "2011-07-15T12:52:02Z"^^xsd:dateTime;
- prov:endedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
-.</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:End provides additional descriptions about the binary prov:wasEndedBy relation from some ended prov:Activity to an prov:Entity that ended it. For example, :ball_game prov:wasEndedBy :buzzer; prov:qualifiedEnd [ a prov:End; prov:entity :buzzer; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- , <a title="http://www.w3.org/ns/prov#EntityInfluence" href="#EntityInfluence" class="owlclass">prov:EntityInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup> , <a title="http://www.w3.org/ns/prov#entity" href="#p_entity">prov:entity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedEnd" href="#qualifiedEnd">prov:qualifiedEnd</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasEndedBy" href="#wasEndedBy" class="owlproperty">prov:wasEndedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-End">End</a> </dd>
- </dl>
- </div>
-
- <div id="Derivation" class="entity">
- <h3 id="x41--------class--prov-derivation-----------------back-to-qualified-classes">
- <span class="xref" id="eg41">(41)</span>
- Class: <a href="#Derivation"><span class="dotted" title="http://www.w3.org/ns/prov#Derivation">prov:Derivation</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Derivation</p>
- <div class="definition"><p>A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-# The simplest (and least detailed) form of derivation.
-:bar_chart
- a prov:Entity;
- prov:wasDerivedFrom :aggregatedByRegions;
-.
-
-# The simple form can be accompanied by a qualified form:
-# which provides more details about how :bar_chart was
-# derived from :aggregatedRegions.
-
-:bar_chart
- a prov:Entity;
-
- prov:wasDerivedFrom :aggregatedByRegions;
- prov:qualifiedDerivation [
- a prov:Derivation;
- prov:entity :aggregatedByRegions;
-
- # Derivations can cite the influencing Activity in doing the derivation.
- prov:hadActivity :create_the_chart;
-
- # They can also cite the Usage and Generation that the Activity
- # performed to generate :bar_chart.
- prov:hadUsage :data_loading;
- prov:hadGeneration :plot_the_chart;
- ];
-.
-
-### The process during which the chart was created, from loading the data to the software, to process the data and plot the chart.
-### Additional metadata was recorded, like when it started (before the usage), ended (after the generation of the chart) and who was associated with it.
-
-:create_the_chart
- a prov:Activity;
- prov:wasAssociatedWith :derek;
- prov:startedAtTime "2012-04-03T00:00:00Z"^^xsd:dateTime;
- prov:endedAtTime "2012-04-03T00:00:10Z"^^xsd:dateTime;
-.
-
-### The final chart was plotted
-
-:plot_the_chart
- a prov:Generation, prov:InstantaneousEvent;
- prov:atTime "2012-04-03T00:00:01Z"^^xsd:dateTime;
-.
-
-### The data was getting used to create the chart
-
-:data_loading
- a prov:Usage;
- prov:atTime "2012-04-03T00:00:00Z"^^xsd:dateTime;
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>The more specific forms of prov:Derivation (i.e., prov:Revision, prov:Quotation, prov:PrimarySource) should be asserted if they apply.</p>
- </dd>
- <dd class="comment"><p>An instance of prov:Derivation provides additional descriptions about the binary prov:wasDerivedFrom relation from some derived prov:Entity to another prov:Entity from which it was derived. For example, :chewed_bubble_gum prov:wasDerivedFrom :unwrapped_bubble_gum; prov:qualifiedDerivation [ a prov:Derivation; prov:entity :unwrapped_bubble_gum; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#EntityInfluence" href="#EntityInfluence" class="owlclass">prov:EntityInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadUsage" href="#hadUsage">prov:hadUsage</a> <sup class="type-op" title="object property">op</sup>
- , <a title="http://www.w3.org/ns/prov#hadGeneration" href="#hadGeneration">prov:hadGeneration</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#entity" href="#p_entity">prov:entity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedDerivation" href="#qualifiedDerivation">prov:qualifiedDerivation</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Revision" href="#Revision" class="owlclass">prov:Revision</a>
- , <a title="http://www.w3.org/ns/prov#PrimarySource" href="#PrimarySource" class="owlclass">prov:PrimarySource</a>
- , <a title="http://www.w3.org/ns/prov#Quotation" href="#Quotation" class="owlclass">prov:Quotation</a>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlproperty">prov:wasDerivedFrom</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Derivation">Derivation</a> </dd>
- </dl>
- </div>
-
- <div id="PrimarySource" class="entity">
- <h3 id="x42--------class--prov-primarysource-----------------back-to-qualified-classes">
- <span class="xref" id="eg42">(42)</span>
- Class: <a href="#PrimarySource"><span class="dotted" title="http://www.w3.org/ns/prov#PrimarySource">prov:PrimarySource</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#PrimarySource</p>
- <div class="definition"><p>A primary source for a topic refers to something produced by some agent with direct experience and knowledge about the topic, at the time of the topic's study, without benefit from hindsight.
-
-Because of the directness of primary sources, they 'speak for themselves' in ways that cannot be captured through the filter of secondary sources. As such, it is important for secondary sources to reference those primary sources from which they were derived, so that their reliability can be investigated.
-
-A primary source relation is a particular case of derivation of secondary materials from their primary sources. It is recognized that the determination of primary sources can be up to interpretation, and should be done according to conventions accepted within the application's domain.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:myPost
- a prov:Entity;
- prov:hadPrimarySource :donQuixote;
- prov:qualifiedPrimarySource [
- a prov:PrimarySource;
- prov:entity :donQuixote;
- :confidenceValue "6"^^xsd:integer;
- rdfs:comment """Not sure if Don Quixote was the original source,
- so asserting a confidence value of 6 out of 10.""";
- ];
-.
-
-:donQuixote a prov:Entity.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:PrimarySource provides additional descriptions about the binary prov:hadPrimarySource relation from some secondary prov:Entity to an earlier, primary prov:Entity. For example, :blog prov:hadPrimarySource :newsArticle; prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :newsArticle; :foo :bar ] .</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadGeneration" href="#hadGeneration">prov:hadGeneration</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#hadUsage" href="#hadUsage">prov:hadUsage</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedPrimarySource" href="#qualifiedPrimarySource">prov:qualifiedPrimarySource</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadPrimarySource" href="#hadPrimarySource" class="owlproperty">prov:hadPrimarySource</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-primary-source">primary-source</a> </dd>
- </dl>
- </div>
-
- <div id="Quotation" class="entity">
- <h3 id="x43--------class--prov-quotation-----------------back-to-qualified-classes">
- <span class="xref" id="eg43">(43)</span>
- Class: <a href="#Quotation"><span class="dotted" title="http://www.w3.org/ns/prov#Quotation">prov:Quotation</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Quotation</p>
- <div class="definition"><p>A quotation is the repeat of (some or all of) an entity, such as text or image, by someone who may or may not be its original author. Quotation is a particular case of derivation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:dagstuhl-quote
- a prov:Entity;
- prov:value "why would people record and share provenance in the first place?";
- prov:wasQuotedFrom <http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>;
- prov:qualifiedQuotation [
- a prov:Quotation;
- prov:entity <http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>;
- ex:fromSection 2;
- ];
- prov:wasAttributedTo <http://data.semanticweb.org/person/luc-moreau>;
-.
-
-<http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>
- a prov:Entity;
- prov:wasAttributedTo <http://data.semanticweb.org/person/paul-groth>;
-.
-
-<http://data.semanticweb.org/person/luc-moreau> a prov:Person, prov:Agent .
-<http://data.semanticweb.org/person/paul-groth> a prov:Person, prov:Agent .
-
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Quotation provides additional descriptions about the binary prov:wasQuotedFrom relation from some taken prov:Entity from an earlier, larger prov:Entity. For example, :here_is_looking_at_you_kid prov:wasQuotedFrom :casablanca_script; prov:qualifiedQuotation [ a prov:Quotation; prov:entity :casablanca_script; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadGeneration" href="#hadGeneration">prov:hadGeneration</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#hadUsage" href="#hadUsage">prov:hadUsage</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedQuotation" href="#qualifiedQuotation">prov:qualifiedQuotation</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasQuotedFrom" href="#wasQuotedFrom" class="owlproperty">prov:wasQuotedFrom</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-quotation">quotation</a> </dd>
- </dl>
- </div>
-
- <div id="Revision" class="entity">
- <h3 id="x44--------class--prov-revision-----------------back-to-qualified-classes">
- <span class="xref" id="eg44">(44)</span>
- Class: <a href="#Revision"><span class="dotted" title="http://www.w3.org/ns/prov#Revision">prov:Revision</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Revision</p>
- <div class="definition"><p>A revision is a derivation for which the resulting entity is a revised version of some original. The implication here is that the resulting entity contains substantial content from the original. Revision is a particular case of derivation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:draft2
- a prov:Entity;
- prov:wasRevisionOf :draft1;
- prov:qualifiedRevision [
- a prov:Revision;
- prov:entity :draft1;
- ex:peerReviewed false;
- ];
-
- prov:wasAssociatedWith :edward;
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :edward;
- prov:hadRole :editor;
- ];
-.
-
-:draft1 a prov:Entity .
-
-:edward
- a prov:Person, prov:Agent;
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Revision provides additional descriptions about the binary prov:wasRevisionOf relation from some newer prov:Entity to an earlier prov:Entity. For example, :draft_2 prov:wasRevisionOf :draft_1; prov:qualifiedRevision [ a prov:Revision; prov:entity :draft_1; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadGeneration" href="#hadGeneration">prov:hadGeneration</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#hadUsage" href="#hadUsage">prov:hadUsage</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedRevision" href="#qualifiedRevision">prov:qualifiedRevision</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasRevisionOf" href="#wasRevisionOf" class="owlproperty">prov:wasRevisionOf</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-revision">revision</a> </dd>
- </dl>
- </div>
-
- <div id="ActivityInfluence" class="entity">
- <h3 id="x45--------class--prov-activityinfluence-----------------back-to-qualified-classes">
- <span class="xref" id="eg45">(45)</span>
- Class: <a href="#ActivityInfluence"><span class="dotted" title="http://www.w3.org/ns/prov#ActivityInfluence">prov:ActivityInfluence</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#ActivityInfluence</p>
- <div class="editors definition"><p>ActivitiyInfluence is the capacity of an activity to have an effect on the character, development, or behavior of another by means of generation, invalidation, communication, or other.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:bar_chart
- a prov:Entity;
- prov:wasGeneratedBy :illustrating;
- prov:qualifiedGeneration :making-bar-chart;
-.
-
-:making-bar-chart
- a prov:Generation,
- prov:ActivityInfluence; ## Instances of Generation, Invalidation and Communication qualify
- prov:activity :illustrating; ## the influence of an Activity (cited by prov:activity)
- rdfs:comment "Ended up with bar chart as line chart looked ugly."@en;
-.
-
-:illustrating a prov:Activity .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>It is not recommended that the type ActivityInfluence be asserted without also asserting one of its more specific subclasses.</p>
- </dd>
- <dd class="comment"><p>ActivityInfluence provides additional descriptions of an Activity's binary influence upon any other kind of resource. Instances of ActivityInfluence use the prov:activity property to cite the influencing Activity.</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#activity" href="#p_activity">prov:activity</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole">prov:hadRole</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#influencer" href="#influencer">prov:influencer</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlclass">prov:Generation</a>
- , <a title="http://www.w3.org/ns/prov#Invalidation" href="#Invalidation" class="owlclass">prov:Invalidation</a>
- , <a title="http://www.w3.org/ns/prov#Communication" href="#Communication" class="owlclass">prov:Communication</a>
- </dd>
- </dl>
- </div>
-
- <div id="Generation" class="entity">
- <h3 id="x46--------class--prov-generation-----------------back-to-qualified-classes">
- <span class="xref" id="eg46">(46)</span>
- Class: <a href="#Generation"><span class="dotted" title="http://www.w3.org/ns/prov#Generation">prov:Generation</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Generation</p>
- <div class="definition"><p>Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix bbc: <http://www.bbc.co.uk/> .
-@prefix eg: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:bbcNews2012-04-03
- a prov:Entity, eg:DailyNews;
- rdfs:comment """The BBC news home page on 2012-04-03 contained a reference
- to a given news item, but the BBC news home page on
- the next day did not.""";
-
- prov:wasGeneratedBy :publishingActivity;
- prov:qualifiedGeneration [
- a prov:Generation, prov:InstantaneousEvent;
- prov:atTime "2012-04-03T00:00:01Z"^^xsd:dateTime;
- prov:activity :publishingActivity;
- ];
- prov:qualifiedInvalidation [
- a prov:Invalidation, prov:InstantaneousEvent;
- prov:atTime "2012-04-03T23:59:59Z"^^xsd:dateTime;
- ];
-.
-
-:publishingActivity
- a prov:Activity;
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Generation provides additional descriptions about the binary prov:wasGeneratedBy relation from a generated prov:Entity to the prov:Activity that generated it. For example, :cake prov:wasGeneratedBy :baking; prov:qualifiedGeneration [ a prov:Generation; prov:activity :baking; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- , <a title="http://www.w3.org/ns/prov#ActivityInfluence" href="#ActivityInfluence" class="owlclass">prov:ActivityInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#activity" href="#p_activity">prov:activity</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#atTime" href="#atTime">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadGeneration" href="#hadGeneration">prov:hadGeneration</a> <sup class="type-op" title="object property">op</sup>
- <a title="http://www.w3.org/ns/prov#qualifiedGeneration" href="#qualifiedGeneration">prov:qualifiedGeneration</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy" class="owlproperty">prov:wasGeneratedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Generation">Generation</a> </dd>
- </dl>
- </div>
-
- <div id="Communication" class="entity">
- <h3 id="x47--------class--prov-communication-----------------back-to-qualified-classes">
- <span class="xref" id="eg47">(47)</span>
- Class: <a href="#Communication"><span class="dotted" title="http://www.w3.org/ns/prov#Communication">prov:Communication</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Communication</p>
- <div class="definition"><p>Communication is the exchange of an entity by two activities, one activity using the entity generated by the other.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:writing-celebrity-gossip
- a prov:Activity;
- prov:wasInformedBy :voicemail-interception;
- prov:qualifiedCommunication :informing-the-journalist;
-.
-
-:informing-the-journalist
- a prov:Communication;
- prov:activity :voicemail-interception;
- ex:mediaType "email";
-.
-
-:voicemail-interception a prov:Activity .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Communication provides additional descriptions about the binary prov:wasInformedBy relation from an informed prov:Activity to the prov:Activity that informed it. For example, :you_jumping_off_bridge prov:wasInformedBy :everyone_else_jumping_off_bridge; prov:qualifiedCommunication [ a prov:Communication; prov:activity :everyone_else_jumping_off_bridge; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#ActivityInfluence" href="#ActivityInfluence" class="owlclass">prov:ActivityInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#activity" href="#p_activity">prov:activity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedCommunication" href="#qualifiedCommunication">prov:qualifiedCommunication</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInformedBy" href="#wasInformedBy" class="owlproperty">prov:wasInformedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Communication">Communication</a> </dd>
- </dl>
- </div>
-
- <div id="Invalidation" class="entity">
- <h3 id="x48--------class--prov-invalidation-----------------back-to-qualified-classes">
- <span class="xref" id="eg48">(48)</span>
- Class: <a href="#Invalidation"><span class="dotted" title="http://www.w3.org/ns/prov#Invalidation">prov:Invalidation</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Invalidation</p>
- <div class="definition"><p>Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix wgs: <http://www.w3.org/2003/01/geo/wgs84_pos#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix foaf: <http://xmlns.com/foaf/0.1/> .
-@prefix : <http://example.com/> .
-
-:the-Painter
- a prov:Entity, :Painting;
- rdfs:label "Le Peintre"@fr, "The Painter"@en;
- prov:wasAttributedTo <http://dbpedia.org/resource/Pablo_Picasso>;
-
- prov:wasInvalidatedBy :swissair_Flight_111_crash;
- prov:qualifiedInvalidation [
- a prov:Invalidation;
- prov:activity :swissair_Flight_111_crash;
- prov:atTime "1998-09-02T01:31:00Z"^^xsd:dateTime;
- prov:atLocation <http://purl.org/twc/location/Swissair-Flight-111-crash>;
- ];
-.
-
-<http://purl.org/twc/location/Swissair-Flight-111-crash>
- a prov:Location;
- wgs:lat 44.409167;
- wgs:long -63.973611;
-.
-
-<http://dbpedia.org/resource/Pablo_Picasso>
- a prov:Agent;
- foaf:depiction <http://upload.wikimedia.org/wikipedia/commons/9/98/Pablo_picasso_1.jpg>;
-.
-
-:swissair_Flight_111_crash
- a prov:Activity;
- prov:used <http://dbpedia.org/resource/Swissair_Flight_111>;
- prov:startedAtTime "1998-09-02T01:31:00Z"^^xsd:dateTime;
- prov:atLocation <http://dbpedia.org/resource/Atlantic_ocean>;
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Invalidation provides additional descriptions about the binary prov:wasInvalidatedBy relation from an invalidated prov:Entity to the prov:Activity that invalidated it. For example, :uncracked_egg prov:wasInvalidatedBy :baking; prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :baking; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- , <a title="http://www.w3.org/ns/prov#ActivityInfluence" href="#ActivityInfluence" class="owlclass">prov:ActivityInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#activity" href="#p_activity">prov:activity</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#atTime" href="#atTime">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedInvalidation" href="#qualifiedInvalidation">prov:qualifiedInvalidation</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy" class="owlproperty">prov:wasInvalidatedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Invalidation">Invalidation</a> </dd>
- </dl>
- </div>
-
- <div id="AgentInfluence" class="entity">
- <h3 id="x49--------class--prov-agentinfluence-----------------back-to-qualified-classes">
- <span class="xref" id="eg49">(49)</span>
- Class: <a href="#AgentInfluence"><span class="dotted" title="http://www.w3.org/ns/prov#AgentInfluence">prov:AgentInfluence</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#AgentInfluence</p>
- <div class="editors definition"><p>AgentInfluence is the capacity of an agent to have an effect on the character, development, or behavior of another by means of attribution, association, delegation, or other.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrating
- a prov:Activity;
- prov:wasAssociatedWith :derek;
- prov:qualifiedAssociation [
- a prov:Association,
- prov:AgentInfluence; ## Instances of Generation, Invalidation and Communication qualify
- prov:agent :derek; ## the influence of an Agent (cited by prov:agent)
- prov:hadRole :illustrationist
- ];
-.
-
-:derek a prov:Person, prov:Agent, prov:Entity .
-
-:illustratonist a prov:Role .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>AgentInfluence provides additional descriptions of an Agent's binary influence upon any other kind of resource. Instances of AgentInfluence use the prov:agent property to cite the influencing Agent.</p>
- </dd>
- <dd class="comment"><p>It is not recommended that the type AgentInfluence be asserted without also asserting one of its more specific subclasses.</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#agent" href="#p_agent">prov:agent</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole">prov:hadRole</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#influencer" href="#influencer">prov:influencer</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Delegation" href="#Delegation" class="owlclass">prov:Delegation</a>
- , <a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlclass">prov:Association</a>
- , <a title="http://www.w3.org/ns/prov#Attribution" href="#Attribution" class="owlclass">prov:Attribution</a>
- </dd>
- </dl>
- </div>
-
- <div id="Attribution" class="entity">
- <h3 id="x50--------class--prov-attribution-----------------back-to-qualified-classes">
- <span class="xref" id="eg50">(50)</span>
- Class: <a href="#Attribution"><span class="dotted" title="http://www.w3.org/ns/prov#Attribution">prov:Attribution</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Attribution</p>
- <div class="definition"><p>Attribution is the ascribing of an entity to an agent.
-
-When an entity e is attributed to agent ag, entity e was generated by some unspecified activity that in turn was associated to agent ag. Thus, this relation is useful when the activity is not known, or irrelevant.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-<http://dbpedia.org/resource/Fallingwater>
- a prov:Entity;
- prov:wasAttributedTo <http://dbpedia.org/resource/Edgar_J._Kaufmann>,
- <http://dbpedia.org/resource/Frank_Lloyd_Wright>,
- :western-Pennsylvania-Conservancy;
- prov:qualifiedAttribution [
- a prov:Attribution;
- prov:agent <http://dbpedia.org/resource/Edgar_J._Kaufmann>;
- ex:hadRole :owner;
- ];
- prov:qualifiedAttribution [
- a prov:Attribution;
- prov:agent <http://dbpedia.org/resource/Frank_Lloyd_Wright>;
- ex:hadRole :architect;
- ];
- prov:qualifiedAttribution [
- a prov:Attribution;
- prov:agent :western-Pennsylvania-Conservancy;
- ex:hadRole :conserver;
- ];
-.
-
-<http://dbpedia.org/resource/Edgar_J._Kaufmann> a prov:Person, prov:Agent .
-<http://dbpedia.org/resource/Frank_Lloyd_Wright> a prov:Person, prov:Agent .
-:western-Pennsylvania-Conservancy a prov:Organization, prov:Agent .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Attribution provides additional descriptions about the binary prov:wasAttributedTo relation from an prov:Entity to some prov:Agent that had some responsible for it. For example, :cake prov:wasAttributedTo :baker; prov:qualifiedAttribution [ a prov:Attribution; prov:entity :baker; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#AgentInfluence" href="#AgentInfluence" class="owlclass">prov:AgentInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#agent" href="#p_agent">prov:agent</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedAttribution" href="#qualifiedAttribution">prov:qualifiedAttribution</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasAttributedTo" href="#wasAttributedTo" class="owlproperty">prov:wasAttributedTo</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribution">attribution</a> </dd>
- </dl>
- </div>
-
- <div id="Association" class="entity">
- <h3 id="x51--------class--prov-association-----------------back-to-qualified-classes">
- <span class="xref" id="eg51">(51)</span>
- Class: <a href="#Association"><span class="dotted" title="http://www.w3.org/ns/prov#Association">prov:Association</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Association</p>
- <div class="definition"><p>An activity association is an assignment of responsibility to an agent for an activity, indicating that the agent had a role in the activity. It further allows for a plan to be specified, which is the plan intended by the agent to achieve some goals in the context of this activity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrating
- a prov:Activity;
- prov:wasAssociatedWith :derek,
- :steve;
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :derek;
- prov:hadRole :illustrationist;
- ];
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :steve;
- prov:hadRole :stylist;
- prov:hadPlan :style-guide;
- rdfs:comment "Steve helped Derek conform with the publisher's style guide."@en;
- ];
-.
-
-:derek a prov:Person, prov:Agent, prov:Entity .
-:steve a prov:Person, prov:Agent, prov:Entity .
-
-:illustratonist a prov:Role .
-:stylist a prov:Role .
-
-:style-guide a prov:Plan, prov:Entity .
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Association provides additional descriptions about the binary prov:wasAssociatedWith relation from an prov:Activity to some prov:Agent that had some responsiblity for it. For example, :baking prov:wasAssociatedWith :baker; prov:qualifiedAssociation [ a prov:Association; prov:agent :baker; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#AgentInfluence" href="#AgentInfluence" class="owlclass">prov:AgentInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadPlan" href="#hadPlan">prov:hadPlan</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole">prov:hadRole</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#agent" href="#p_agent">prov:agent</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedAssociation" href="#qualifiedAssociation">prov:qualifiedAssociation</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasAssociatedWith" href="#wasAssociatedWith" class="owlproperty">prov:wasAssociatedWith</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Association">Association</a> </dd>
- </dl>
- </div>
-
- <div id="Plan" class="entity">
- <h3 id="x52--------class--prov-plan-----------------back-to-qualified-classes">
- <span class="xref" id="eg52">(52)</span>
- Class: <a href="#Plan"><span class="dotted" title="http://www.w3.org/ns/prov#Plan">prov:Plan</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Plan</p>
- <div class="definition"><p>A plan is an entity that represents a set of actions or steps intended by one or more agents to achieve some goals.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrating
- a prov:Activity;
- prov:qualifiedAssociation :steve-checking-style-guide;
-.
-
-:steve-checking-style-guide
- a prov:Association;
- prov:agent :steve;
- prov:hadPlan :style-guide;
- rdfs:comment "Steve followed the publisher's style guide"@en;
-.
-
-:style-guide
- a prov:Plan, prov:Entity;
- rdfs:comment "Use blue graphs for positive spin, red for negative"@en;
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>There exist no prescriptive requirement on the nature of plans, their representation, the actions or steps they consist of, or their intended goals. Since plans may evolve over time, it may become necessary to track their provenance, so plans themselves are entities. Representing the plan explicitly in the provenance can be useful for various tasks: for example, to validate the execution as represented in the provenance record, to manage expectation failures, or to provide explanations.</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadPlan" href="#hadPlan">prov:hadPlan</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Association">Association</a> </dd>
- </dl>
- </div>
-
- <div id="Delegation" class="entity">
- <h3 id="x53--------class--prov-delegation-----------------back-to-qualified-classes">
- <span class="xref" id="eg53">(53)</span>
- Class: <a href="#Delegation"><span class="dotted" title="http://www.w3.org/ns/prov#Delegation">prov:Delegation</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Delegation</p>
- <div class="definition"><p>Delegation is the assignment of authority and responsibility to an agent (by itself or by another agent) to carry out a specific activity as a delegate or representative, while the agent it acts on behalf of retains some responsibility for the outcome of the delegated work.
-
-For example, a student acted on behalf of his supervisor, who acted on behalf of the department chair, who acted on behalf of the university; all those agents are responsible in some way for the activity that took place but we do not say explicitly who bears responsibility and to what degree.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-### In this example, Frank (an insurance agent) acts on behalf of his company for performing
-### a policy sale
-
-:policySale
- a prov:Activity;
- prov:wasAssociatedWith :insuranceAgent_Frank;
-.
-
-:insuranceAgent_Frank
- a prov:Person;
- prov:actedOnBehalfOf :insuranceCompany_A;
- prov:qualifiedDelegation [
- a prov:Delegation;
- prov:agent :insuranceCompany_A;
- ex:rewardScheme "commission";
- prov:hadActivity :policySale ;
- ];
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instance of prov:Delegation provides additional descriptions about the binary prov:actedOnBehalfOf relation from a performing prov:Agent to some prov:Agent for whom it was performed. For example, :mixing prov:wasAssociatedWith :toddler . :toddler prov:actedOnBehalfOf :mother; prov:qualifiedDelegation [ a prov:Delegation; prov:entity :mother; :foo :bar ].</p>
- </dd>
-
- <dt>is subclass of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#AgentInfluence" href="#AgentInfluence" class="owlclass">prov:AgentInfluence</a>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity">prov:hadActivity</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#agent" href="#p_agent">prov:agent</a> <sup class="type-op" title="object property">op</sup> </dd>
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation">prov:qualifiedDelegation</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf" class="owlproperty">prov:actedOnBehalfOf</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-delegation">delegation</a> </dd>
- </dl>
- </div>
-
- <div id="InstantaneousEvent" class="entity">
- <h3 id="x54--------class--prov-instantaneousevent-----------------back-to-qualified-classes">
- <span class="xref" id="eg54">(54)</span>
- Class: <a href="#InstantaneousEvent"><span class="dotted" title="http://www.w3.org/ns/prov#InstantaneousEvent">prov:InstantaneousEvent</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#InstantaneousEvent</p>
- <div class="definition"><p>The PROV data model is implicitly based on a notion of instantaneous events (or just events), that mark transitions in the world. Events include generation, usage, or invalidation of entities, as well as starting or ending of activities. This notion of event is not first-class in the data model, but it is useful for explaining its other concepts and its semantics.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix bbc: <http://www.bbc.co.uk/> .
-@prefix : <http://example.com/> .
-
-:bbcNews2012-04-03
- a prov:Entity, :DailyNews;
- rdfs:comment """The BBC news home page on 2012-04-03 contained
- a reference to a given news item, but the BBC news
- home page on the next day did not.""";
-
- prov:qualifiedGeneration [
- a prov:Generation, prov:InstantaneousEvent;
- prov:atTime "2012-04-03T00:00:01Z"^^xsd:dateTime;
- ];
- prov:qualifiedInvalidation [
- a prov:Invalidation, prov:InstantaneousEvent;
- prov:atTime "2012-04-03T23:59:59Z"^^xsd:dateTime;
- ];
-.
-</pre>
- </div>
-
- <dl class="description">
- <dd class="comment"><p>An instantaneous event, or event for short, happens in the world and marks a change in the world, in its activities and in its entities. The term 'event' is commonly used in process algebra with a similar meaning. Events represent communications or interactions; they are assumed to be atomic and instantaneous.</p>
- </dd>
- <dt>described with properties:</dt><dd></dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#atTime" href="#atTime">prov:atTime</a> <sup class="type-dp" title="data property">dp</sup>
- </dd>
-
- <dt></dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole">prov:hadRole</a> <sup class="type-op" title="object property">op</sup> , <a title="http://www.w3.org/ns/prov#atLocation" href="#atLocation">prov:atLocation</a> <sup class="type-op" title="object property">op</sup>
- </dd><dt>has subclasses</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlclass">prov:Generation</a>
- , <a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlclass">prov:Start</a>
- , <a title="http://www.w3.org/ns/prov#Invalidation" href="#Invalidation" class="owlclass">prov:Invalidation</a>
- , <a title="http://www.w3.org/ns/prov#End" href="#End" class="owlclass">prov:End</a>
- , <a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlclass">prov:Usage</a>
- </dd>
- </dl>
- </div>
-
- <div id="Role" class="entity">
- <h3 id="x55--------class--prov-role-----------------back-to-qualified-classes">
- <span class="xref" id="eg55">(55)</span>
- Class: <a href="#Role"><span class="dotted" title="http://www.w3.org/ns/prov#Role">prov:Role</span></a>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified classes</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Role</p>
- <div class="definition"><p>A role is the function of an entity or agent with respect to an activity, in the context of a usage, generation, invalidation, association, start, and end.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:divideActivity
- a prov:Activity;
- prov:used :variableA, :variableB;
-
- prov:qualifiedUsage [
- a prov:Usage;
- prov:entity :variableA;
- prov:hadRole :dividend;
- ];
- prov:qualifiedUsage [
- a prov:Usage;
- prov:entity :variableB;
- prov:hadRole :divisor;
- ];
-
- prov:generated :result_112234;
-.
-
-:variableA
- a prov:Entity;
- prov:value 10;
-.
-:variableB
- a prov:Entity;
- prov:value 2;
-.
-
-:dividend a prov:Role.
-:divisor a prov:Role.
-
-:result_112234
- a prov:Entity;
- prov:value 5;
- prov:wasGeneratedBy :divideActivity;
-.
-</pre>
- </div>
-
- <dl class="description">
-
- <dt>in range of</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole">prov:hadRole</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribute-role">attribute-role</a> </dd>
- </dl>
- </div>
-</div>
-<div class="prov-qualified owl-properties crossreference" >
- <div id="wasInfluencedBy" class="entity">
- <h3 id="x56--------property--prov-wasinfluencedby-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg56">(56)</span>
- Property: <a href="#wasInfluencedBy"><span class="dotted" title="http://www.w3.org/ns/prov#wasInfluencedBy">prov:wasInfluencedBy</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#wasInfluencedBy</p>
- <div class="definition def-from-2"><p>Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrationActivity
- a prov:Activity;
- prov:used :aggregatedByRegions;
- prov:wasAssociatedWith :derek;
- prov:wasInformedBy :aggregationActivity;
-.
-
-:illustrationActivity
- a prov:Activity;
- prov:wasInfluencedBy :aggregatedByRegions, # prov:wasInfluencedBy is a superproperty of
- :derek, # many of the direct binary
- :aggregationActivity; # PROV-O properties.
-.
-
-:aggregationActivity a prov:Activity .
-:derek a prov:Agent .
-:aggregatedByRegions a prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>Because prov:wasInfluencedBy is a broad relation, its more specific subproperties (e.g. prov:wasInformedBy, prov:actedOnBehalfOf, prov:wasEndedBy, etc.) should be used when applicable.</p>
- </div>
- <div class="comment "><p>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- or <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- or <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- or <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- or <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has sub-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#hadMember" href="#hadMember" class="owlclass">prov:hadMember</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasAttributedTo" href="#wasAttributedTo" class="owlclass">prov:wasAttributedTo</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasAssociatedWith" href="#wasAssociatedWith" class="owlclass">prov:wasAssociatedWith</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy" class="owlclass">prov:wasGeneratedBy</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlclass">prov:wasDerivedFrom</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy" class="owlclass">prov:wasInvalidatedBy</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#used" href="#used" class="owlclass">prov:used</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf" class="owlclass">prov:actedOnBehalfOf</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasInformedBy" href="#wasInformedBy" class="owlclass">prov:wasInformedBy</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasStartedBy" href="#wasStartedBy" class="owlclass">prov:wasStartedBy</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#wasEndedBy" href="#wasEndedBy" class="owlclass">prov:wasEndedBy</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlproperty">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-influence">influence</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedInfluence" class="entity">
- <h3 id="x57--------property--prov-qualifiedinfluence-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg57">(57)</span>
- Property: <a href="#qualifiedInfluence"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedInfluence">prov:qualifiedInfluence</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedInfluence</p>
- <div class="definition def-from-2"><p>Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix my: <http://example.com/ontology#> .
-@prefix : <http://example.com/> .
-
-# Although domain extension 'my:wasConductedBy' is not defined by PROV-O,
-# the relation between a surgery and an agent can still be qualified
-# by reusing prov:Influence and one of its three subclasses:
-# AgentInfluence, EntityInfluence, and ActivityInfluence
-# (depending on the type of the influencing object).
-
-:conductingSurgery_1
- a prov:Activity;
-
- # This unqualified influence is unknown in PROV;
- # it would be a subproperty of prov:wasAssociatedWith.
- my:wasConductedBy :bob;
- prov:wasInfluencedBy :bob;
- prov:qualifiedInfluence [
- # Even though PROV systems do not understand my:wasConductedBy,
- # they will at least understand that :bob influenced the
- # surgery in some way.
- a prov:Influence; # Inferred
- prov:agent :bob; # The object of my:wasConductedBy
-
- # Domain extension properties may be used to describe the
- # influences that an Entity, Activity, or Agent
- # have upon another Entity, Activity, or Agent.
- my:degree .72;
- ];
-.
-
-:bob a prov:Agent .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>Because prov:qualifiedInfluence is a broad relation, the more specific relations (qualifiedCommunication, qualifiedDelegation, qualifiedEnd, etc.) should be used when applicable.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- or <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- or <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </li>
- </ul>
- </dd>
-
- <dt>has sub-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedAssociation" href="#qualifiedAssociation" class="owlclass">prov:qualifiedAssociation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedRevision" href="#qualifiedRevision" class="owlclass">prov:qualifiedRevision</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInvalidation" href="#qualifiedInvalidation" class="owlclass">prov:qualifiedInvalidation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedPrimarySource" href="#qualifiedPrimarySource" class="owlclass">prov:qualifiedPrimarySource</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedDerivation" href="#qualifiedDerivation" class="owlclass">prov:qualifiedDerivation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedGeneration" href="#qualifiedGeneration" class="owlclass">prov:qualifiedGeneration</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedUsage" href="#qualifiedUsage" class="owlclass">prov:qualifiedUsage</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedQuotation" href="#qualifiedQuotation" class="owlclass">prov:qualifiedQuotation</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedStart" href="#qualifiedStart" class="owlclass">prov:qualifiedStart</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedAttribution" href="#qualifiedAttribution" class="owlclass">prov:qualifiedAttribution</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedEnd" href="#qualifiedEnd" class="owlclass">prov:qualifiedEnd</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedCommunication" href="#qualifiedCommunication" class="owlclass">prov:qualifiedCommunication</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation" class="owlclass">prov:qualifiedDelegation</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlproperty">prov:wasInfluencedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-influence">influence</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedGeneration" class="entity">
- <h3 id="x58--------property--prov-qualifiedgeneration-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg58">(58)</span>
- Property: <a href="#qualifiedGeneration"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedGeneration">prov:qualifiedGeneration</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedGeneration</p>
- <div class="definition def-from-2"><p>Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:bar_chart
- a prov:Entity;
- prov:wasGeneratedBy :illustrating;
- prov:qualifiedGeneration [
- a prov:Generation;
- prov:activity :illustrating;
- rdfs:comment "Ended up with bar chart as line chart looked ugly."@en;
- ];
-.
-
-:illustrating a prov:Activity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Activity prov:generated Entity :e, then it can qualify how it performed the Generation using prov:qualifiedGeneration [ a prov:Generation; prov:entity :e; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlclass">prov:Generation</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy" class="owlproperty">prov:wasGeneratedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Generation">Generation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedDerivation" class="entity">
- <h3 id="x59--------property--prov-qualifiedderivation-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg59">(59)</span>
- Property: <a href="#qualifiedDerivation"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedDerivation">prov:qualifiedDerivation</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedDerivation</p>
- <div class="definition def-from-2"><p>A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:bar_chart
- a prov:Entity;
- prov:wasDerivedFrom :aggregatedByRegions;
- prov:qualifiedDerivation [
- a prov:Derivation;
- prov:entity :aggregatedByRegions;
-
- ## More details about the activity underpinning the derivation
- prov:hadGeneration :chat_plotting;
- prov:hadActivity :chart_creation ;
- ];
-.
-
-### The process of creating the chart, from loading the data, to process it, and plot it to end users
-
-:chart_creation
- a prov:Activity ;
- prov:wasAssociatedWith :derek;
- prov:startedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:endedAtTime "2011-07-16T03:00:02Z"^^xsd:dateTime;
-.
-
-#### Now the chart is plotted
-
-:chat_plotting
- a prov:Generation ;
- prov:atTime "2011-07-16T03:00:02Z"^^xsd:dateTime;
-.
-
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Entity prov:wasDerivedFrom Entity :e, then it can qualify how it was derived using prov:qualifiedDerivation [ a prov:Derivation; prov:entity :e; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlproperty">prov:wasDerivedFrom</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Derivation">Derivation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedPrimarySource" class="entity">
- <h3 id="x60--------property--prov-qualifiedprimarysource-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg60">(60)</span>
- Property: <a href="#qualifiedPrimarySource"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedPrimarySource">prov:qualifiedPrimarySource</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedPrimarySource</p>
- <div class="definition def-from-2"><p>A primary source for a topic refers to something produced by some agent with direct experience and knowledge about the topic, at the time of the topic's study, without benefit from hindsight.
-
-Because of the directness of primary sources, they 'speak for themselves' in ways that cannot be captured through the filter of secondary sources. As such, it is important for secondary sources to reference those primary sources from which they were derived, so that their reliability can be investigated.
-
-A primary source relation is a particular case of derivation of secondary materials from their primary sources. It is recognized that the determination of primary sources can be up to interpretation, and should be done according to conventions accepted within the application's domain.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix dcterms: <http://purl.org/dc/terms/> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:temperatureDisplay
- a prov:Entity;
- prov:hadPrimarySource :sensorReading20120510;
- prov:qualifiedPrimarySource [
- a prov:PrimarySource;
- prov:entity :sensorReading20120510;
- ex:precisionLoss true;
- rdfs:comment """The displayed temperature does not show the full precision
- available in the reading.""";
- ];
-.
-
-:sensorReading20120510
- a prov:Entity;
- prov:wasGeneratedBy :temperatureSensor;
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Entity prov:hadPrimarySource Entity :e, then it can qualify how using prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :e; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#PrimarySource" href="#PrimarySource" class="owlclass">prov:PrimarySource</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#hadPrimarySource" href="#hadPrimarySource" class="owlproperty">prov:hadPrimarySource</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-primary-source">primary-source</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedQuotation" class="entity">
- <h3 id="x61--------property--prov-qualifiedquotation-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg61">(61)</span>
- Property: <a href="#qualifiedQuotation"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedQuotation">prov:qualifiedQuotation</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedQuotation</p>
- <div class="definition def-from-2"><p>A quotation is the repeat of (some or all of) an entity, such as text or image, by someone who may or may not be its original author. Quotation is a particular case of derivation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix my: <http://example.com/vocab/my#> .
-@prefix : <http://example.com/> .
-
-:bl-dagstuhl
- a prov:Entity;
- prov:value """During the workshop, it became clear to me that the consensus
- based models (which are often graphical in nature) can not only be
- formalized but also be directly connected to these database focused
- formalizations. I just needed to get over the differences in syntax.
- This could imply that we could have nice way to trace provenance across
- systems and through databases and be able to understand the
- mathematical properties of this interconnection.""";
- prov:wasQuotedFrom <http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>;
- prov:qualifiedQuotation [
- a prov:Quotation;
- prov:entity <http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>;
- my:fromSection 1;
- ];
-.
-
-<http://purl.org/twc/page/thoughts-from-the-dagstuhl-workshop>
- a prov:Entity;
- prov:wasAttributedTo <http://data.semanticweb.org/person/paul-groth>;
-.
-
-<http://data.semanticweb.org/person/luc-moreau> a prov:Person, prov:Agent .
-<http://data.semanticweb.org/person/paul-groth> a prov:Person, prov:Agent .
-
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Entity prov:wasQuotedFrom Entity :e, then it can qualify how using prov:qualifiedQuotation [ a prov:Quotation; prov:entity :e; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Quotation" href="#Quotation" class="owlclass">prov:Quotation</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasQuotedFrom" href="#wasQuotedFrom" class="owlproperty">prov:wasQuotedFrom</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-quotation">quotation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedRevision" class="entity">
- <h3 id="x62--------property--prov-qualifiedrevision-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg62">(62)</span>
- Property: <a href="#qualifiedRevision"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedRevision">prov:qualifiedRevision</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedRevision</p>
- <div class="definition def-from-2"><p>A revision is a derivation for which the resulting entity is a revised version of some original. The implication here is that the resulting entity contains substantial content from the original. Revision is a particular case of derivation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:draft2
- a prov:Entity;
- prov:wasRevisionOf :draft1;
- prov:qualifiedRevision [
- a prov:Revision;
- prov:entity :draft1
- ];
- prov:wasAttributedTo :eddie;
-.
-
-:draft1 a prov:Entity .
-:eddie a prov:Person, prov:Agent, prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Entity prov:wasRevisionOf Entity :e, then it can qualify how it was revised using prov:qualifiedRevision [ a prov:Revision; prov:entity :e; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Revision" href="#Revision" class="owlclass">prov:Revision</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasRevisionOf" href="#wasRevisionOf" class="owlproperty">prov:wasRevisionOf</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-revision">revision</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedAttribution" class="entity">
- <h3 id="x63--------property--prov-qualifiedattribution-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg63">(63)</span>
- Property: <a href="#qualifiedAttribution"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedAttribution">prov:qualifiedAttribution</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedAttribution</p>
- <div class="definition def-from-2"><p>Attribution is the ascribing of an entity to an agent.
-
-When an entity e is attributed to agent ag, entity e was generated by some unspecified activity that in turn was associated to agent ag. Thus, this relation is useful when the activity is not known, or irrelevant.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-## When the role of the agent is not known or does not matter:
-
-:nationalRegionsList
- a prov:Entity;
- prov:wasAttributedTo :civil_action_group;
-.
-
-:civil_action_group a prov:Agent .
-
-## If we want to express the role of the agent:
-
-:nationalRegionsList
- a prov:Entity;
- prov:qualifiedAttribution [
- a prov:Attribution;
- prov:agent :civil_action_group;
- ex:hadRole :owner;
- ]
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Entity prov:wasAttributedTo Agent :ag, then it can qualify how it was influenced using prov:qualifiedAttribution [ a prov:Attribution; prov:agent :ag; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Attribution" href="#Attribution" class="owlclass">prov:Attribution</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasAttributedTo" href="#wasAttributedTo" class="owlproperty">prov:wasAttributedTo</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribution">attribution</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedInvalidation" class="entity">
- <h3 id="x64--------property--prov-qualifiedinvalidation-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg64">(64)</span>
- Property: <a href="#qualifiedInvalidation"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedInvalidation">prov:qualifiedInvalidation</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedInvalidation</p>
- <div class="definition def-from-2"><p>Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/ontology#> .
-@prefix : <http://example.com/> .
-
-:the-Painter
- a prov:Entity, ex:Painting;
- rdfs:label "Le Peintre"@fr, "The Painter"@en;
- prov:wasAttributedTo <http://dbpedia.org/resource/Pablo_Picasso>;
-
- prov:wasInvalidatedBy :swissair_Flight_111_crash;
- prov:qualifiedInvalidation [
- a prov:Invalidation;
- prov:activity :swissair_Flight_111_crash;
- prov:atTime "1998-09-02T01:31:00Z"^^xsd:dateTime;
- prov:atLocation <http://purl.org/twc/location/Swissair-Flight-111-crash>;
- ];
-.
-
-:swissair_Flight_111_crash a prov:Activity .
-<http://purl.org/twc/location/Swissair-Flight-111-crash> a prov:Location .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Entity prov:wasInvalidatedBy Activity :a, then it can qualify how it was invalidated using prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :a; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Invalidation" href="#Invalidation" class="owlclass">prov:Invalidation</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy" class="owlproperty">prov:wasInvalidatedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Invalidation">Invalidation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedStart" class="entity">
- <h3 id="x65--------property--prov-qualifiedstart-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg65">(65)</span>
- Property: <a href="#qualifiedStart"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedStart">prov:qualifiedStart</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedStart</p>
- <div class="definition def-from-2"><p>Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-# Start can be used to qualify wasStartedBy with time and location information.
-
-:consistency_checking
- a prov:Activity;
- prov:wasStartedBy :updated_data_record;
- prov:qualifiedStart [
- a prov:Start;
- prov:entity :updated_data_record;
- prov:atTime "2011-07-06T01:48:36Z"^^xsd:dateTime;
- prov:atLocation :scienceLab_003;
- prov:hadActivity :syntax_checking;
- ];
-.
-
-:updated_data_record a prov:Entity .
-
-### There is an explicit process of checking the syntax of the updated data record
-
-:syntax_checking
- a prov:Activity ;
- prov:startedAtTime "2011-07-06T01:48:36Z"^^xsd:dateTime;
- prov:endedAtTime "2011-07-06T02:12:36Z"^^xsd:dateTime;
- prov:wasAssociatedWith :syntax_checker ;
-.
-
-:syntax_checker a prov:SoftwareAgent .</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Activity prov:wasStartedBy Entity :e1, then it can qualify how it was started using prov:qualifiedStart [ a prov:Start; prov:entity :e1; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlclass">prov:Start</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasStartedBy" href="#wasStartedBy" class="owlproperty">prov:wasStartedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Start">Start</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedUsage" class="entity">
- <h3 id="x66--------property--prov-qualifiedusage-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg66">(66)</span>
- Property: <a href="#qualifiedUsage"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedUsage">prov:qualifiedUsage</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedUsage</p>
- <div class="definition def-from-2"><p>Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:newsPublication
- a prov:Activity;
- prov:used :tsunami_image;
- prov:qualifiedUsage [
- a prov:Usage;
- prov:entity :tsunami_image;
- ex:hasCopyrightPermission :licensedUse;
- ex:hasOwner :reuters;
- ];
-.
-
-:tsunami_image a prov:Entity .
-:reuters a prov:Agent .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Activity prov:used Entity :e, then it can qualify how it used it using prov:qualifiedUsage [ a prov:Usage; prov:entity :e; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlclass">prov:Usage</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#used" href="#used" class="owlproperty">prov:used</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Usage">Usage</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedCommunication" class="entity">
- <h3 id="x67--------property--prov-qualifiedcommunication-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg67">(67)</span>
- Property: <a href="#qualifiedCommunication"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedCommunication">prov:qualifiedCommunication</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedCommunication</p>
- <div class="definition def-from-2"><p>Communication is the exchange of an entity by two activities, one activity using the entity generated by the other.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:writing-celebrity-gossip
- a prov:Activity;
- prov:wasAssociatedWith :journalist;
- prov:wasInformedBy :voicemail-interception;
- prov:qualifiedCommunication [
- a prov:Communication;
- prov:activity :voicemail-interception;
- rdfs:comment """The journalist was informed by the private
- investigator, but we don't know how or what he was told."""@en;
- ];
-.
-
-:voicemail-interception
- a prov:Activity;
- prov:wasAssociatedWith :private-investigator;
-.
-
-:private-investigator a prov:Agent .
-:journalist a prov:Agent .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Activity prov:wasInformedBy Activity :a, then it can qualify how it was influenced using prov:qualifiedCommunication [ a prov:Communication; prov:activity :a; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Communication" href="#Communication" class="owlclass">prov:Communication</a>
- </li>
- </ul>
- </dd>
-
- <dt>can be qualified with</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Communication" href="#Communication" class="owlclass">prov:Communication</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Communication">Communication</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedAssociation" class="entity">
- <h3 id="x68--------property--prov-qualifiedassociation-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg68">(68)</span>
- Property: <a href="#qualifiedAssociation"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedAssociation">prov:qualifiedAssociation</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedAssociation</p>
- <div class="definition def-from-2"><p>An activity association is an assignment of responsibility to an agent for an activity, indicating that the agent had a role in the activity. It further allows for a plan to be specified, which is the plan intended by the agent to achieve some goals in the context of this activity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrating
- a prov:Activity;
- prov:wasAssociatedWith :derek,
- :steve;
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :derek;
- prov:hadRole :illustrationist;
- rdfs:comment "Derek made the illustration"@en
- ];
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :steve;
- prov:hadRole :stylist;
- prov:hadPlan :style-guide;
- rdfs:comment "Steve helped Derek conform with the publisher's style guide."@en
- ];
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :derek;
- prov:hadRole :stylist;
- rdfs:comment "But Derek also did some styling of his own."@en
- ] .
-
-:derek a prov:Person, prov:Agent .
-:steve a prov:Person, prov:Agent .
-
-:illustratonist a prov:Role .
-:stylist a prov:Role .
-
-:style-guide a prov:Plan, prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Activity prov:wasAssociatedWith Agent :ag, then it can qualify the Association using prov:qualifiedAssociation [ a prov:Association; prov:agent :ag; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlclass">prov:Association</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasAssociatedWith" href="#wasAssociatedWith" class="owlproperty">prov:wasAssociatedWith</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Association">Association</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedEnd" class="entity">
- <h3 id="x69--------property--prov-qualifiedend-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg69">(69)</span>
- Property: <a href="#qualifiedEnd"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedEnd">prov:qualifiedEnd</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedEnd</p>
- <div class="definition def-from-2"><p>End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-### End can be used to qualify wasEndedBy with time and location information
-
-:experiment
- a prov:Activity;
- prov:wasEndedBy :inconsistentResult;
- prov:qualifiedEnd [
- a prov:End;
- prov:entity :inconsistentResult;
- prov:atTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:atLocation :scienceLab_003;
- prov:hadActivity :analyse_intermediate_result ;
- ];
-.
-
-:inconsistentResult a prov:Entity .
-
-### An implicit process of analysing the intermediate result to confirm its expected consistency
-
-analyse_intermediate_result
- a prov:Activity ;
- prov:startedAtTime "2011-07-15T12:52:02Z"^^xsd:dateTime;
- prov:endedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
-.</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Activity prov:wasEndedBy Entity :e1, then it can qualify how it was ended using prov:qualifiedEnd [ a prov:End; prov:entity :e1; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#End" href="#End" class="owlclass">prov:End</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#wasEndedBy" href="#wasEndedBy" class="owlproperty">prov:wasEndedBy</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-End">End</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="qualifiedDelegation" class="entity">
- <h3 id="x70--------property--prov-qualifieddelegation-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg70">(70)</span>
- Property: <a href="#qualifiedDelegation"><span class="dotted" title="http://www.w3.org/ns/prov#qualifiedDelegation">prov:qualifiedDelegation</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#qualifiedDelegation</p>
- <div class="definition def-from-2"><p>Delegation is the assignment of authority and responsibility to an agent (by itself or by another agent) to carry out a specific activity as a delegate or representative, while the agent it acts on behalf of retains some responsibility for the outcome of the delegated work.
-
-For example, a student acted on behalf of his supervisor, who acted on behalf of the department chair, who acted on behalf of the university; all those agents are responsible in some way for the activity that took place but we do not say explicitly who bears responsibility and to what degree.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:traffic-stop
- a prov:Activity;
- prov:wasAssociatedWith :chauffeur,
- :traffic-officer-34;
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :chauffeur;
-
- # The chauffeur was the one violating traffic rules.
- prov:hadRole :violator;
- ];
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :traffic-officer-34;
-
- # The officer was the one enforcing the traffic rules.
- prov:hadRole :enforcer;
- ];
-.
-
-:chauffeur
- a prov:Person;
- prov:actedOnBehalfOf :celebrity-in-car;
- prov:qualifiedDelegation [
- a prov:Delegation;
- prov:agent :celebrity-in-car;
-
- # The celebrity employed the chauffeur during the enforcement.
- prov:hadRole :employer;
- prov:hadActivity :driving-during-the-year ;
- ];
-.
-
-#The chaffeur was employed for a whole year as a driver
-:driving-during-the-year a prov:Activity ;
- prov:wasAssociatedWith :chaffeur;
- prov:qualifiedAssociation [
- a prov:Association;
- prov:hadRole :driver;
- ];
- prov:startedAtTime "2011-07-16T01:52:02Z"^^xsd:dateTime;
- prov:endedAtTime "2012-07-16T01:52:02Z"^^xsd:dateTime;;
-.
-
-:traffic_officer_34
- a prov:Person;
- prov:actedOnBehalfOf :city-of-Paris;
- prov:qualifiedDelegation [
- a prov:Delegation;
- prov:agent :city-of-Paris;
-
- # The city of Paris employed the officer during the enforcement.
- prov:hadRole :employer;
- prov:hadActivity :control-city-traffic ;
- ];
-.
-
-:control-city-traffic a prov:Activity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>If this Agent prov:actedOnBehalfOf Agent :ag, then it can qualify how with prov:qualifiedResponsibility [ a prov:Responsibility; prov:agent :ag; :foo :bar ].</p>
- </div>
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlclass">prov:qualifiedInfluence</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Delegation" href="#Delegation" class="owlclass">prov:Delegation</a>
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf" class="owlproperty">prov:actedOnBehalfOf</a> <sup class="type-op" title="object property">op</sup>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-delegation">delegation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="influencer" class="entity">
- <h3 id="x71--------property--prov-influencer-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg71">(71)</span>
- Property: <a href="#influencer"><span class="dotted" title="http://www.w3.org/ns/prov#influencer">prov:influencer</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#influencer</p>
- <div class="definition def-from-7"><p>This property is used as part of the qualified influence pattern. Subclasses of prov:Influence use these subproperties to reference the resource (Entity, Agent, or Activity) whose influence is being qualified.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrationActivity
- a prov:Activity;
- prov:qualifiedUsage :illustration_usage;
- prov:qualifiedAssociation :illustration_association;
- prov:qualifiedCommunication :illustration_communication;
-.
-
-:illustration_usage
- a prov:Usage;
- prov:entity :aggregatedByRegions;
- prov:influencer :aggregatedByRegions; # Inferred
-.
-
-:illustration_association
- a prov:Association;
- prov:agent :derek;
- prov:influencer :derek; # - - - - - - - Inferred
-.
-
-:illustration_communication
- a prov:Communication;
- prov:activity :aggregationActivity;
- prov:influencer :aggregationActivity; # Inferred
-.
-
-:aggregationActivity a prov:Activity .
-:derek a prov:Agent .
-:aggregatedByRegions a prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>Subproperties of prov:influencer are used to cite the object of an unqualified PROV-O triple whose predicate is a subproperty of prov:wasInfluencedBy (e.g. prov:used, prov:wasGeneratedBy). prov:influencer is used much like rdf:object is used.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- </li>
- </ul>
- </dd>
-
- <dt>has sub-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#agent" href="#p_agent" class="owlclass">prov:agent</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlclass">prov:entity</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#activity" href="#p_activity" class="owlclass">prov:activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-influence">influence</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="p_entity" class="entity">
- <h3 id="x72--------property--prov-entity-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg72">(72)</span>
- Property: <a href="#p_entity"><span class="dotted" title="http://www.w3.org/ns/prov#entity">prov:entity</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#entity</p>
- <div class="definition def-from-7"><p>The prov:entity property references an prov:Entity which influenced a resource. This property applies to an prov:EntityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:world-literature-homework-submission-32
- a prov:Entity;
- prov:hadPrimarySource :donQuixote;
- prov:qualifiedPrimarySource [
- a prov:PrimarySource;
- prov:entity :donQuixote;
- # Other attributes of the relationship
- ];
-.
-
-:donQuixote a prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#influencer" href="#influencer" class="owlclass">prov:influencer</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#EntityInfluence" href="#EntityInfluence" class="owlclass">prov:EntityInfluence</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlclass">prov:Entity</a>
- </li>
- </ul>
- </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="hadUsage" class="entity">
- <h3 id="x73--------property--prov-hadusage-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg73">(73)</span>
- Property: <a href="#hadUsage"><span class="dotted" title="http://www.w3.org/ns/prov#hadUsage">prov:hadUsage</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#hadUsage</p>
- <div class="definition def-from-2"><p>Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-:digestedProteinSample1
- a prov:Entity;
- prov:wasDerivedFrom :proteinSample;
- prov:qualifiedDerivation [
- a prov:Derivation;
- prov:hadUsage [
- a prov:Usage;
- prov:entity :Trypsin;
- prov:hadRole :treatmentEnzyme;
- ];
- ];
- prov:entity :proteinSample;
-.
-:proteinSample a prov:Entity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The _optional_ Usage involved in an Entity's Derivation.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlclass">prov:Usage</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Usage">Usage</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="hadGeneration" class="entity">
- <h3 id="x74--------property--prov-hadgeneration-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg74">(74)</span>
- Property: <a href="#hadGeneration"><span class="dotted" title="http://www.w3.org/ns/prov#hadGeneration">prov:hadGeneration</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#hadGeneration</p>
- <div class="definition def-from-2"><p>Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix ex: <http://example.com/vocab#> .
-@prefix : <http://example.com/> .
-
-:bar_chart
- a prov:Entity, ex:Chart;
- prov:wasDerivedFrom :aggregatedByRegions;
- prov:qualifiedDerivation [
- a prov:Derivation;
- prov:entity :aggregatedByRegions;
- prov:hadGeneration :illustration;
- ];
-.
-
-:aggregatedByRegions a ex:Dataset .
-
-:illustration
- a prov:Generation,
- prov:InstantaneousEvent;
- prov:activity :illustrationActivity;
- prov:atTime "2012-04-03T00:00:11Z"^^xsd:dateTime;
-.
-
-:illustrationActivity
- a prov:Activity;
- prov:startedAtTime "2012-04-03T00:00:00Z"^^xsd:dateTime;
- prov:endedAtTime "2012-04-03T00:00:25Z"^^xsd:dateTime;
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The _optional_ Generation involved in an Entity's Derivation.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlclass">prov:Generation</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Generation">Generation</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="p_activity" class="entity">
- <h3 id="x75--------property--prov-activity-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg75">(75)</span>
- Property: <a href="#p_activity"><span class="dotted" title="http://www.w3.org/ns/prov#activity">prov:activity</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#activity</p>
- <div class="definition def-from-7"><p>The prov:activity property references an prov:Activity which influenced a resource. This property applies to an prov:ActivityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:making-bar-chart
- a prov:Generation,
- prov:ActivityInfluence;
- prov:activity :illustrating;
- rdfs:comment "Ended up with bar chart as line chart looked ugly."@en;
-.
-
-:illustrating a prov:Activity .
-
-:bar_chart
- a prov:Entity;
- prov:wasGeneratedBy :illustrating;
- prov:qualifiedGeneration :making-bar-chart;
-.
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#influencer" href="#influencer" class="owlclass">prov:influencer</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#ActivityInfluence" href="#ActivityInfluence" class="owlclass">prov:ActivityInfluence</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="p_agent" class="entity">
- <h3 id="x76--------property--prov-agent-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg76">(76)</span>
- Property: <a href="#p_agent"><span class="dotted" title="http://www.w3.org/ns/prov#agent">prov:agent</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#agent</p>
- <div class="definition def-from-7"><p>The prov:agent property references an prov:Agent which influenced a resource. This property applies to an prov:AgentInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:world_flight_1937
- a prov:Activity;
-
- prov:wasAssociatedWith <http://dbpedia.org/resource/Amelia_Earhart>,
- <http://dbpedia.org/resource/Purdue_University>,
- <http://dbpedia.org/resource/Lockheed_Aircraft_Company>;
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent <http://dbpedia.org/resource/Amelia_Earhart>;
- prov:hadRole :pilot;
- ];
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent <http://dbpedia.org/resource/Purdue_University>;
- prov:hadRole :financer;
- ];
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent <http://dbpedia.org/resource/Lockheed_Aircraft_Company>;
- prov:hadRole :plane_builder;
- ];
-
- rdfs:seeAlso <http://en.wikipedia.org/wiki/Amelia_Earhart#1937_world_flight>;
-.
-
-<http://dbpedia.org/resource/Amelia_Earhart> a prov:Person, prov:Agent .
-<http://dbpedia.org/resource/Purdue_University> a prov:Organization, prov:Agent .
-<http://dbpedia.org/resource/Lockheed_Aircraft_Company> a prov:Organization, prov:Agent .
-
-</pre>
- </div>
-
- <div class="description">
- <dl>
-
- <dt>has super-properties</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#influencer" href="#influencer" class="owlclass">prov:influencer</a> <sup class="type-op" title="object property">op</sup>
- </li>
- </ul>
- </dd>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#AgentInfluence" href="#AgentInfluence" class="owlclass">prov:AgentInfluence</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlclass">prov:Agent</a>
- </li>
- </ul>
- </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="hadPlan" class="entity">
- <h3 id="x77--------property--prov-hadplan-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg77">(77)</span>
- Property: <a href="#hadPlan"><span class="dotted" title="http://www.w3.org/ns/prov#hadPlan">prov:hadPlan</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#hadPlan</p>
- <div class="definition def-from-2"><p>A plan is an entity that represents a set of actions or steps intended by one or more agents to achieve some goals.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:illustrating
- a prov:Activity;
- prov:wasAssociatedWith :derek,
- :steve;
- prov:qualifiedAssociation [
- a prov:Association;
- prov:agent :steve;
- prov:hadRole :stylist;
- prov:hadPlan :style-guide;
- rdfs:comment "Steve followed the style guide"@en;
- ];
-.
-
-:style-guide
- a prov:Plan, prov:Entity;
- rdfs:comment "Use blue graphs for positive spin, red for negative"@en;
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The _optional_ Plan adopted by an Agent in Association with some Activity. Plan specifications are out of the scope of this specification.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlclass">prov:Association</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Plan" href="#Plan" class="owlclass">prov:Plan</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Association">Association</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="hadActivity" class="entity">
- <h3 id="x78--------property--prov-hadactivity-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg78">(78)</span>
- Property: <a href="#hadActivity"><span class="dotted" title="http://www.w3.org/ns/prov#hadActivity">prov:hadActivity</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#hadActivity</p>
- <div class="definition def-from-2"><p>An activity is something that occurs over a period of time and acts upon or with entities; it may include consuming, processing, transforming, modifying, relocating, using, or generating entities.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-# The activity that which used, generated, invalidated
-# or was responsible for the entity. In this qualified Derivation
-# prov:hadActivity references the activity that generated the bar chart.
-
-:bar_chart
- a prov:Entity;
- prov:wasDerivedFrom :aggregatedByRegions;
- prov:wasGeneratedBy :make_bar_chart;
- prov:qualifiedDerivation [
- a prov:Derivation;
- prov:entity :aggregatedByRegions;
- prov:hadActivity :make_bar_chart; # references same activity as prov:wasGeneratedBy
- ];
-.
-
-:aggregatedByRegions a prov:Entity .
-:make_bar_chart a prov:Activity .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The _optional_ Activity of an Influence, which used, generated, invalidated, or was the responsibility of some Entity. This property is _not_ used by ActivityInfluence (use prov:activity instead).</p>
- </div>
- <div class="comment "><p>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Delegation" href="#Delegation" class="owlclass">prov:Delegation</a>
- or <a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlclass">prov:Derivation</a>
- or <a title="http://www.w3.org/ns/prov#End" href="#End" class="owlclass">prov:End</a>
- or <a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlclass">prov:Start</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlclass">prov:Activity</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-Activity">Activity</a> </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="atTime" class="entity">
- <h3 id="x79--------property--prov-attime-dp-----------------back-to-qualified-properties">
- <span class="xref" id="eg79">(79)</span>
- Property: <a href="#atTime"><span class="dotted" title="http://www.w3.org/ns/prov#atTime">prov:atTime</span></a> <sup class="type-dp" title="data property">dp</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#atTime</p>
- <div class="definition def-from-2"><p>The PROV data model is implicitly based on a notion of instantaneous events (or just events), that mark transitions in the world. Events include generation, usage, or invalidation of entities, as well as starting or ending of activities. This notion of event is not first-class in the data model, but it is useful for explaining its other concepts and its semantics.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:Timearticle20120430_publication
- a prov:InstantaneousEvent;
- prov:atTime "2012-04-30T20:40:40"^^xsd:dateTime;
-.
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The time at which an InstantaneousEvent occurred, in the form of xsd:dateTime.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- http://www.w3.org/2001/XMLSchema#dateTime
- </li>
- </ul>
- </dd>
-
- <dt>qualifies</dt>
- <dd>
- <a title="http://www.w3.org/ns/prov#invalidatedAtTime" href="#invalidatedAtTime" class="owlproperty">prov:invalidatedAtTime</a> <sup class="type-dp" title="data property">dp</sup>
- </dd>
-
- </dl>
- </div>
- </div>
-
- <div id="hadRole" class="entity">
- <h3 id="x80--------property--prov-hadrole-op-----------------back-to-qualified-properties">
- <span class="xref" id="eg80">(80)</span>
- Property: <a href="#hadRole"><span class="dotted" title="http://www.w3.org/ns/prov#hadRole">prov:hadRole</span></a> <sup class="type-op" title="object property">op</sup>
- <span class="backlink">
- back to <a href="#prov-qualified-owl-terms-at-a-glance">qualified properties</a>
- </span>
- </h3>
- <p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#hadRole</p>
- <div class="definition def-from-2"><p>A role is the function of an entity or agent with respect to an activity, in the context of a usage, generation, invalidation, association, start, and end.</p>
- </div>
-
- <div class="example">
- <strong class="crossreference">Example</strong>
- <pre>@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-@prefix : <http://example.com/> .
-
-:divideActivity
- a prov:Activity;
-
- prov:used :variableA;
- prov:qualifiedUsage [
- a prov:Usage;
- prov:entity :variableA;
- prov:hadRole :dividend;
- ];
-
- prov:used :variableB;
- prov:qualifiedUsage [
- a prov:Usage;
- prov:entity :variableB;
- prov:hadRole :divisor;
- ];
-.
-
-:variableA a prov:Entity .
-:variableB a prov:Entity .
-
-:dividend a prov:Role .
-:divisor a prov:Role .
-</pre>
- </div>
-
- <div class="description">
- <div class="comment "><p>The _optional_ Role that an Entity assumed in the context of an Activity. For example, :baking prov:used :spoon; prov:qualified [ a prov:Usage; prov:entity :spoon; prov:hadRole roles:mixing_implement ].</p>
- </div>
- <div class="comment "><p>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</p>
- </div>
- <dl>
-
- <dt>has domain</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlclass">prov:Association</a>
- or <a title="http://www.w3.org/ns/prov#InstantaneousEvent" href="#InstantaneousEvent" class="owlclass">prov:InstantaneousEvent</a>
- </li>
- <li>
- <a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlclass">prov:Influence</a>
- </li>
- </ul>
- </dd>
-
- <dt>has range</dt>
- <dd>
- <ul>
- <li>
- <a title="http://www.w3.org/ns/prov#Role" href="#Role" class="owlclass">prov:Role</a>
- </li>
- </ul>
- </dd>
-
- <dt>PROV-DM term</dt>
- <dd>
- <a title="prov-dm" href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/Overview.html#term-attribute-role">attribute-role</a> </dd>
-
- </dl>
- </div>
- </div>
-
-</div>
-
- </div>
-
- <div id="cross-reference-index" class="section">
- <h3><span class="secno">4.4 </span>Term Index</h3>
- <p>The PROV-O terms in this cross reference are shown below alphabetically, along with their entry number.</p>
- <div>
- <table>
- <caption id="xref-table"><a href="#cross-reference-index">Table 4</a>: Term Index.</caption>
- <tbody><tr>
- <th>PROV-O Term</th>
- <th>Position within Cross Reference</th>
- </tr>
- <tr>
- <td><a href="#actedOnBehalfOf">actedOnBehalfOf</a></td>
- <td><a href="#actedOnBehalfOf">Entry 12</a></td>
- </tr>
- <tr>
- <td><a href="#Activity">Activity</a></td>
- <td><a href="#Activity">Entry 2</a></td>
- </tr>
- <tr>
- <td><a href="#p_activity">activity</a></td>
- <td><a href="#p_activity">Entry 75</a></td>
- </tr>
- <tr>
- <td><a href="#ActivityInfluence">ActivityInfluence</a></td>
- <td><a href="#ActivityInfluence">Entry 45</a></td>
- </tr>
- <tr>
- <td><a href="#Agent">Agent</a></td>
- <td><a href="#Agent">Entry 3</a></td>
- </tr>
- <tr>
- <td><a href="#p_agent">agent</a></td>
- <td><a href="#p_agent">Entry 76</a></td>
- </tr>
- <tr>
- <td><a href="#AgentInfluence">AgentInfluence</a></td>
- <td><a href="#AgentInfluence">Entry 49</a></td>
- </tr>
- <tr>
- <td><a href="#alternateOf">alternateOf</a></td>
- <td><a href="#alternateOf">Entry 20</a></td>
- </tr>
- <tr>
- <td><a href="#Association">Association</a></td>
- <td><a href="#Association">Entry 51</a></td>
- </tr>
- <tr>
- <td><a href="#atLocation">atLocation</a></td>
- <td><a href="#atLocation">Entry 34</a></td>
- </tr>
- <tr>
- <td><a href="#atTime">atTime</a></td>
- <td><a href="#atTime">Entry 79</a></td>
- </tr>
- <tr>
- <td><a href="#Attribution">Attribution</a></td>
- <td><a href="#Attribution">Entry 50</a></td>
- </tr>
- <tr>
- <td><a href="#Bundle">Bundle</a></td>
- <td><a href="#Bundle">Entry 15</a></td>
- </tr>
- <tr>
- <td><a href="#Collection">Collection</a></td>
- <td><a href="#Collection">Entry 13</a></td>
- </tr>
- <tr>
- <td><a href="#Communication">Communication</a></td>
- <td><a href="#Communication">Entry 47</a></td>
- </tr>
- <tr>
- <td><a href="#Delegation">Delegation</a></td>
- <td><a href="#Delegation">Entry 53</a></td>
- </tr>
- <tr>
- <td><a href="#Derivation">Derivation</a></td>
- <td><a href="#Derivation">Entry 41</a></td>
- </tr>
- <tr>
- <td><a href="#EmptyCollection">EmptyCollection</a></td>
- <td><a href="#EmptyCollection">Entry 14</a></td>
- </tr>
- <tr>
- <td><a href="#End">End</a></td>
- <td><a href="#End">Entry 40</a></td>
- </tr>
- <tr>
- <td><a href="#endedAtTime">endedAtTime</a></td>
- <td><a href="#endedAtTime">Entry 10</a></td>
- </tr>
- <tr>
- <td><a href="#Entity">Entity</a></td>
- <td><a href="#Entity">Entry 1</a></td>
- </tr>
- <tr>
- <td><a href="#p_entity">entity</a></td>
- <td><a href="#p_entity">Entry 72</a></td>
- </tr>
- <tr>
- <td><a href="#EntityInfluence">EntityInfluence</a></td>
- <td><a href="#EntityInfluence">Entry 37</a></td>
- </tr>
- <tr>
- <td><a href="#generated">generated</a></td>
- <td><a href="#generated">Entry 35</a></td>
- </tr>
- <tr>
- <td><a href="#generatedAtTime">generatedAtTime</a></td>
- <td><a href="#generatedAtTime">Entry 22</a></td>
- </tr>
- <tr>
- <td><a href="#Generation">Generation</a></td>
- <td><a href="#Generation">Entry 46</a></td>
- </tr>
- <tr>
- <td><a href="#hadActivity">hadActivity</a></td>
- <td><a href="#hadActivity">Entry 78</a></td>
- </tr>
- <tr>
- <td><a href="#hadGeneration">hadGeneration</a></td>
- <td><a href="#hadGeneration">Entry 74</a></td>
- </tr>
- <tr>
- <td><a href="#hadMember">hadMember</a></td>
- <td><a href="#hadMember">Entry 29</a></td>
- </tr>
- <tr>
- <td><a href="#hadPlan">hadPlan</a></td>
- <td><a href="#hadPlan">Entry 77</a></td>
- </tr>
- <tr>
- <td><a href="#hadPrimarySource">hadPrimarySource</a></td>
- <td><a href="#hadPrimarySource">Entry 23</a></td>
- </tr>
- <tr>
- <td><a href="#hadRole">hadRole</a></td>
- <td><a href="#hadRole">Entry 80</a></td>
- </tr>
- <tr>
- <td><a href="#hadUsage">hadUsage</a></td>
- <td><a href="#hadUsage">Entry 73</a></td>
- </tr>
- <tr>
- <td><a href="#Influence">Influence</a></td>
- <td><a href="#Influence">Entry 36</a></td>
- </tr>
- <tr>
- <td><a href="#influenced">influenced</a></td>
- <td><a href="#influenced">Entry 33</a></td>
- </tr>
- <tr>
- <td><a href="#influencer">influencer</a></td>
- <td><a href="#influencer">Entry 71</a></td>
- </tr>
- <tr>
- <td><a href="#InstantaneousEvent">InstantaneousEvent</a></td>
- <td><a href="#InstantaneousEvent">Entry 54</a></td>
- </tr>
- <tr>
- <td><a href="#invalidated">invalidated</a></td>
- <td><a href="#invalidated">Entry 32</a></td>
- </tr>
- <tr>
- <td><a href="#invalidatedAtTime">invalidatedAtTime</a></td>
- <td><a href="#invalidatedAtTime">Entry 27</a></td>
- </tr>
- <tr>
- <td><a href="#Invalidation">Invalidation</a></td>
- <td><a href="#Invalidation">Entry 48</a></td>
- </tr>
- <tr>
- <td><a href="#Location">Location</a></td>
- <td><a href="#Location">Entry 19</a></td>
- </tr>
- <tr>
- <td><a href="#Organization">Organization</a></td>
- <td><a href="#Organization">Entry 18</a></td>
- </tr>
- <tr>
- <td><a href="#Person">Person</a></td>
- <td><a href="#Person">Entry 16</a></td>
- </tr>
- <tr>
- <td><a href="#Plan">Plan</a></td>
- <td><a href="#Plan">Entry 52</a></td>
- </tr>
- <tr>
- <td><a href="#PrimarySource">PrimarySource</a></td>
- <td><a href="#PrimarySource">Entry 42</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedAssociation">qualifiedAssociation</a></td>
- <td><a href="#qualifiedAssociation">Entry 68</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedAttribution">qualifiedAttribution</a></td>
- <td><a href="#qualifiedAttribution">Entry 63</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedCommunication">qualifiedCommunication</a></td>
- <td><a href="#qualifiedCommunication">Entry 67</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedDelegation">qualifiedDelegation</a></td>
- <td><a href="#qualifiedDelegation">Entry 70</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedDerivation">qualifiedDerivation</a></td>
- <td><a href="#qualifiedDerivation">Entry 59</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedEnd">qualifiedEnd</a></td>
- <td><a href="#qualifiedEnd">Entry 69</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedGeneration">qualifiedGeneration</a></td>
- <td><a href="#qualifiedGeneration">Entry 58</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedInfluence">qualifiedInfluence</a></td>
- <td><a href="#qualifiedInfluence">Entry 57</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedInvalidation">qualifiedInvalidation</a></td>
- <td><a href="#qualifiedInvalidation">Entry 64</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedPrimarySource">qualifiedPrimarySource</a></td>
- <td><a href="#qualifiedPrimarySource">Entry 60</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedQuotation">qualifiedQuotation</a></td>
- <td><a href="#qualifiedQuotation">Entry 61</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedRevision">qualifiedRevision</a></td>
- <td><a href="#qualifiedRevision">Entry 62</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedStart">qualifiedStart</a></td>
- <td><a href="#qualifiedStart">Entry 65</a></td>
- </tr>
- <tr>
- <td><a href="#qualifiedUsage">qualifiedUsage</a></td>
- <td><a href="#qualifiedUsage">Entry 66</a></td>
- </tr>
- <tr>
- <td><a href="#Quotation">Quotation</a></td>
- <td><a href="#Quotation">Entry 43</a></td>
- </tr>
- <tr>
- <td><a href="#Revision">Revision</a></td>
- <td><a href="#Revision">Entry 44</a></td>
- </tr>
- <tr>
- <td><a href="#Role">Role</a></td>
- <td><a href="#Role">Entry 55</a></td>
- </tr>
- <tr>
- <td><a href="#SoftwareAgent">SoftwareAgent</a></td>
- <td><a href="#SoftwareAgent">Entry 17</a></td>
- </tr>
- <tr>
- <td><a href="#specializationOf">specializationOf</a></td>
- <td><a href="#specializationOf">Entry 21</a></td>
- </tr>
- <tr>
- <td><a href="#Start">Start</a></td>
- <td><a href="#Start">Entry 39</a></td>
- </tr>
- <tr>
- <td><a href="#startedAtTime">startedAtTime</a></td>
- <td><a href="#startedAtTime">Entry 7</a></td>
- </tr>
- <tr>
- <td><a href="#Usage">Usage</a></td>
- <td><a href="#Usage">Entry 38</a></td>
- </tr>
- <tr>
- <td><a href="#used">used</a></td>
- <td><a href="#used">Entry 8</a></td>
- </tr>
- <tr>
- <td><a href="#value">value</a></td>
- <td><a href="#value">Entry 24</a></td>
- </tr>
- <tr>
- <td><a href="#wasAssociatedWith">wasAssociatedWith</a></td>
- <td><a href="#wasAssociatedWith">Entry 11</a></td>
- </tr>
- <tr>
- <td><a href="#wasAttributedTo">wasAttributedTo</a></td>
- <td><a href="#wasAttributedTo">Entry 6</a></td>
- </tr>
- <tr>
- <td><a href="#wasDerivedFrom">wasDerivedFrom</a></td>
- <td><a href="#wasDerivedFrom">Entry 5</a></td>
- </tr>
- <tr>
- <td><a href="#wasEndedBy">wasEndedBy</a></td>
- <td><a href="#wasEndedBy">Entry 31</a></td>
- </tr>
- <tr>
- <td><a href="#wasGeneratedBy">wasGeneratedBy</a></td>
- <td><a href="#wasGeneratedBy">Entry 4</a></td>
- </tr>
- <tr>
- <td><a href="#wasInfluencedBy">wasInfluencedBy</a></td>
- <td><a href="#wasInfluencedBy">Entry 56</a></td>
- </tr>
- <tr>
- <td><a href="#wasInformedBy">wasInformedBy</a></td>
- <td><a href="#wasInformedBy">Entry 9</a></td>
- </tr>
- <tr>
- <td><a href="#wasInvalidatedBy">wasInvalidatedBy</a></td>
- <td><a href="#wasInvalidatedBy">Entry 28</a></td>
- </tr>
- <tr>
- <td><a href="#wasQuotedFrom">wasQuotedFrom</a></td>
- <td><a href="#wasQuotedFrom">Entry 25</a></td>
- </tr>
- <tr>
- <td><a href="#wasRevisionOf">wasRevisionOf</a></td>
- <td><a href="#wasRevisionOf">Entry 26</a></td>
- </tr>
- <tr>
- <td><a href="#wasStartedBy">wasStartedBy</a></td>
- <td><a href="#wasStartedBy">Entry 30</a></td>
- </tr>
- </tbody></table>
-</div>
-
- </div>
-
- </div>
-
- <!--section class="appendix">
- <h2>Changes Since First Public Working Draft</h2>
- <ul>
- <li>2012-01-18: hadParticipant was replaced with wasAssociatedWith. Restyled domain/range diagrams.</li>
- <li>2012-01-17: Recipe changed to Plan, linked to Association
- (formerly Control)</li>
- <li>2012-01-16: Added Agent subclasses Person, Organization
- and SoftwareAgent
- <li>2012-01-16: Added alternateOf and specializationOf
- <li>2012-01-18: Replaced wasControlledBy with wasAssociatedWith relation
- <li>2012-01-19: Added wasStartedBy and wasEndedBy relations
- </ul>
- </section-->
-
- <div id="owl-profile" class="appendix informative section">
- <!--OddPage--><h2><span class="secno">A. </span>PROV-O OWL Profile</h2><p><em>This section is non-normative.</em></p>
-
- <p>To encourage widespread adoption, PROV-O's design is intentionally minimal and lightweight.
- Because the OWL 2 RL profile is aimed at RDF applications that require scalable reasoning without sacrificing too much expressive power [<cite><a class="bibref" rel="biblioentry" href="#bib-OWL2-PRIMER">OWL2-PRIMER</a></cite>],
- it served as a baseline for all axioms included in PROV-O. The PROV-O axioms that do not suit the OWL 2 RL profile are listed in
- <a href="#owl-rl-violations">Table 5</a>.
-
- All five use an anonymous <em>class union</em> for the domain or range of a property, while OWL 2 RL requires the classes to be explicitly named.
- Although introducing "placeholder" classes would have suited the
- OWL 2 RL profile, these additional "abstract" classes would have been irrelevant
- to the modeling of provenance information, increased the size of PROV-O unnecessarily, and exposed a potential to confuse users.
- All five axioms listed in the following table <em>use a non-superclass expression in a position that requires a superclass expression</em>
- and do not conform to the OWL 2 RL Profile.
- </p>
-
-<!-- The following table is generated by executing the following from a checked out version of http://dvcs.w3.org/hg/prov/file/tip/ontology
- java -jar bin/profilechecker.jar ProvenanceOntology.owl OWL2RLProfile 2>&1 | python bin/rlplus-justify.py
--->
-<div style="text-align: center">
- <table id="owl-rl-violations">
- <caption><a href="#owl-rl-violations">Table 5</a>: All OWL Axioms in PROV-O that do not conform to the OWL-RL profile.</caption>
- <tbody><tr>
- <th>Non OWL-RL PROV-O Axiom
- </th></tr>
- <tr>
- <td><a href="#atLocation" class="qname">prov:atLocation</a> rdfs:domain <span class="name">[ owl:unionOf (prov:Activity prov:Agent prov:Entity prov:InstantaneousEvent) ]</span></td>
- </tr> <!-- 1 -->
-
- <tr>
- <td><a href="#wasInfluencedBy" class="qname">prov:wasInfluencedBy</a> rdfs:domain <span class="name">[ owl:unionOf (prov:Activity prov:Agent prov:Entity) ]</span></td>
- </tr> <!-- 5 -->
-
- <tr>
- <td><a href="#wasInfluencedBy" class="qname">prov:wasInfluencedBy</a> rdfs:range <span class="name">[ owl:unionOf (prov:Activity prov:Agent prov:Entity) ]</span></td>
- </tr> <!-- 2 -->
-
- <tr>
- <td><a href="#hadActivity" class="qname">prov:hadActivity</a> rdfs:domain <span class="name">[ owl:unionOf (prov:Delegation prov:Derivation prov:Start prov:End) ]</span></td>
- </tr> <!-- 3 -->
-
- <tr>
- <td><a href="#hadRole" class="qname">prov:hadRole</a> rdfs:domain <span class="name">[ owl:unionOf (prov:Association prov:InstantaneousEvent) ]</span></td>
- </tr> <!-- 4 -->
-
- </tbody></table>
-</div>
- <p>
- To provide guidance for OWL 2 RL environments that ignore the union domain axioms, some
- property domains or ranges have also been defined with the closest
- common superclass for the classes in the union, as shown in the following table.
- </p>
-
- <div style="text-align: center">
- <table id="owl-rl-extra-domains">
- <caption><a href="#owl-rl-extra-domains">Table 6</a>: Intersecting OWL2 RL compatible domains/ranges</caption>
- <tbody><tr>
- <th>Property</th> <th>Direction</th> <th>Domain/range</th>
- </tr>
- <tr>
- <td><a href="#atLocation" class="qname">prov:atLocation</a></td>
- <td>rdfs:domain</td>
- <td>(implied: <span class="name">owl:Thing</span>)</td>
- </tr>
-
- <tr>
- <td><a href="#wasInfluencedBy" class="qname">prov:wasInfluencedBy</a></td>
- <td>rdfs:domain / rdfs:range</td>
- <td>(implied: <span class="name">owl:Thing</span>)
- </td></tr>
-
- <tr>
- <td><a href="#hadActivity" class="qname">prov:hadActivity</a></td>
- <td>rdfs:domain</td>
- <td><a href="#Influence" class="qname">prov:Influence</a></td>
- </tr>
-
- <tr>
- <td><a href="#hadRole" class="qname">prov:hadRole</a></td>
- <td>rdfs:domain</td>
- <td><a href="#Influence" class="qname">prov:Influence</a></td>
- </tr>
- </tbody></table>
- </div>
-
- <p>
- Multiple RDFS domains and ranges [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-SCHEMA">RDF-SCHEMA</a></cite>] for a property are
- <a href="http://www.w3.org/TR/2004/REC-rdf-schema-20040210/#ch_range">interpreted as an intersection</a>,
- and thus the above do not provide any additional
- information in an OWL 2 DL or OWL 2 Full profile, which also understands
- the unions. The more general domain should not be
- interpreted as saying, e.g.,
- "<span class="qname">prov:hadActivity</span> can be used with any <span class="qname">prov:Influence</span>",
- but as
- "Anything using <span class="qname">prov:hadActivity</span> is (at least) a prov:Influence".
- </p>
- </div>
-
- <div class="appendix section" id="inverse-names">
- <!--OddPage--><h2><span class="secno">B. </span>Names of inverse properties</h2>
- <p>To maximize interoperability, PROV-O intentionally avoids defining too many properties' inverses.
- In fact, it only defines two (<a class="qname" href="#generated">prov:generated</a> and <a class="qname" href="#invalidated">prov:invalidated</a>).
- When all inverses are defined for all properties, modelers may choose from two logically equivalent properties when making each assertion.
- Although the two options may be logically equivalent, developers consuming the assertions may need to exert extra effort to handle both
- (e.g., by either adding an OWL reasoner or writing code and queries to handle both cases).
- This extra effort can be reduced by preferring one inverse over another.
- </p>
-
- <div class="exampleOuter" >
- <p>For example, the first PROV-O statement (below) could just as easily be asserted as the second statement.
- But if a client queries using <a class="qname" href="#wasDerivedFrom">prov:wasDerivedFrom</a> when <span class="repeated">:hadDerivation</span>
- was used in the assertion, no results will be returned unless OWL reasoning is applied (or the size of the query is doubled).
- </p>
- <pre class="example"><http://www.w3.org/TR/prov-o/> prov:wasDerivedFrom <http://www.w3.org/TR/prov-dm/> .
-
- # These two statements are equivalent if prov:wasDerivedFrom is an inverse of :hadDerivation.
- # But extra effort is required to handle both cases (if one is not already using OWL reasoning).
- # We cannot assume that everybody is using OWL reasoning.
- # We do not want people to write more code and query than necessary.
-
-<http://www.w3.org/TR/prov-dm/> :hadDerivation <http://www.w3.org/TR/prov-o/> .</pre>
- </div>
-
- <p>So, PROV-O avoids this situation by encouraging modelers to use one property instead of its inverse; the preferred property to use is the one defined in the PROV-O ontology. Those asserting and querying for the preferred property avoid the need for OWL reasoning, additional code, and larger queries while maintaining the same level of interoperability.
- </p>
-
- <p>However, the <strong>absence</strong> of defined inverses can lead to a <strong>different</strong> risk to interoperability.
- Because modelers are free to create their own properties to suit their needs,
- they may be motivated to assert the inverse of any PROV-O property defined herein.
- </p>
-
- <div class="exampleOuter" >
- <p>For example, since PROV-O does not define the inverse of <a class="qname" href="#wasDerivedFrom">prov:wasDerivedFrom</a>,
- and if three developers would rather model their assertions in the opposite direction, the following set of assertions might be found in the future web of provenance.
- These assertions are not in an interoperable form without the use of an OWL reasoner, additional code, or larger queries.
- </p>
- <pre class="example"># If PROV-O's properties' inverses are not defined, modelers may be motivated to introduce their own inverse property name.
-# The following three statements are equivalent if their predicates are all inverses of prov:wasDerivedFrom.
-
-<http://www.w3.org/TR/prov-dm/> my:hadDerivation <http://www.w3.org/TR/prov-o/> .
-<http://www.w3.org/TR/prov-dm/> your:ledTo <http://www.w3.org/TR/prov-o/> .
-<http://www.w3.org/TR/prov-dm/> their:derivedTo <http://www.w3.org/TR/prov-o/> .</pre>
- </div>
-
- <p>To balance these two interoperability risks, this document reserves the names of the PROV-O inverses.
- The name of a property's inverse is determined by appending the value of its <span class="repeated">http://www.w3.org/ns/prov#inverse</span>
- annotation to the PROV namespace (<span class="repeated">http://www.w3.org/ns/prov#</span>).
- Modelers wishing to use inverses of the properties defined by PROV-O <em class="rfc2119" title="should">should</em> use those reserved by this document.
- </p>
-
- <div class="exampleOuter" >
- <p>For example, the same three modelers above that defined <code>my:hadDerivation</code>, <code>your:ledTo</code>, and <code>their:derivedTo</code> should instead look for the <span class="repeated">http://www.w3.org/ns/prov#inverse</span> annotation on <a class="qname" href="#wasDerivedFrom">prov:wasDerivedFrom</a> to determine that they should use the property <span class="repeated">http://www.w3.org/ns/prov#hadDerivation</span>.
- </p>
- <pre class="example">@prefix prov: <http://www.w3.org/ns/prov#> .
-
-# Each PROV-O property is annotated with the local name of its inverse.
-
-prov:wasDerivedFrom
- a owl:ObjectProperty;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#>;
- prov:inverse "hadDerivation";
- rdfs:domain prov:Entity;
- rdfs:range prov:Entity;
-.
-
-# Instead of defining their own, modelers should use the
-# recommended inverse local name within the PROV namespace:
-
-<http://www.w3.org/TR/prov-dm/> prov:hadDerivation <http://www.w3.org/TR/prov-o/> .
-
-# Following this recommendation avoids a proliferation of inverse definitions,
-# while encouraging the use of one inverse over another.
-# This increases interoperability.</pre>
- </div>
-
- <p>The following table lists the recommended inverse names that should be used if a modeler does not want to use the recommended PROV-O property.
- For convenience, <a href="http://www.w3.org/ns/prov-o-inverses">this file</a> lists the resulting inverse properties.
- </p>
-
-
-<div id="inverse-names-table">
-<table class="inverse-names">
- <caption><a href="#inverse-names-table">Table 5</a>: Names of inverses</caption>
- <tr>
- <th>Domain</th>
- <th>PROV-O Property</th>
- <th>Recommended inverse name</th>
- <th>Range</th>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlproperty">prov:Agent</a></td>
- <td><a title="http://www.w3.org/ns/prov#actedOnBehalfOf" href="#actedOnBehalfOf" class="owlproperty">prov:actedOnBehalfOf</a></td>
- <td>prov:hadDelegate</td>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlproperty">prov:Agent</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#ActivityInfluence" href="#ActivityInfluence" class="owlproperty">prov:ActivityInfluence</a></td>
- <td><a title="http://www.w3.org/ns/prov#activity" href="#p_activity" class="owlproperty">prov:activity</a></td>
- <td>prov:activityOfInfluence</td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#AgentInfluence" href="#AgentInfluence" class="owlproperty">prov:AgentInfluence</a></td>
- <td><a title="http://www.w3.org/ns/prov#agent" href="#p_agent" class="owlproperty">prov:agent</a></td>
- <td>prov:agentOfInfluence</td>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlproperty">prov:Agent</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#alternateOf" href="#alternateOf" class="owlproperty">prov:alternateOf</a></td>
- <td>prov:alternateOf</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td>union</td>
- <td><a title="http://www.w3.org/ns/prov#atLocation" href="#atLocation" class="owlproperty">prov:atLocation</a></td>
- <td>prov:locationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Location" href="#Location" class="owlproperty">prov:Location</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#EntityInfluence" href="#EntityInfluence" class="owlproperty">prov:EntityInfluence</a></td>
- <td><a title="http://www.w3.org/ns/prov#entity" href="#p_entity" class="owlproperty">prov:entity</a></td>
- <td>prov:entityOfInfluence</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#generated" href="#generated" class="owlproperty">prov:generated</a></td>
- <td>prov:wasGeneratedBy</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td>union</td>
- <td><a title="http://www.w3.org/ns/prov#hadActivity" href="#hadActivity" class="owlproperty">prov:hadActivity</a></td>
- <td>prov:wasActivityOfInfluence</td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlproperty">prov:Derivation</a></td>
- <td><a title="http://www.w3.org/ns/prov#hadGeneration" href="#hadGeneration" class="owlproperty">prov:hadGeneration</a></td>
- <td>prov:generatedAsDerivation</td>
- <td><a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlproperty">prov:Generation</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Collection" href="#Collection" class="owlproperty">prov:Collection</a></td>
- <td><a title="http://www.w3.org/ns/prov#hadMember" href="#hadMember" class="owlproperty">prov:hadMember</a></td>
- <td>prov:wasMemberOf</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlproperty">prov:Association</a></td>
- <td><a title="http://www.w3.org/ns/prov#hadPlan" href="#hadPlan" class="owlproperty">prov:hadPlan</a></td>
- <td>prov:wasPlanOf</td>
- <td><a title="http://www.w3.org/ns/prov#Plan" href="#Plan" class="owlproperty">prov:Plan</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#hadPrimarySource" href="#hadPrimarySource" class="owlproperty">prov:hadPrimarySource</a></td>
- <td>prov:wasPrimarySourceOf</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td>union</td>
- <td><a title="http://www.w3.org/ns/prov#hadRole" href="#hadRole" class="owlproperty">prov:hadRole</a></td>
- <td>prov:wasRoleIn</td>
- <td><a title="http://www.w3.org/ns/prov#Role" href="#Role" class="owlproperty">prov:Role</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlproperty">prov:Derivation</a></td>
- <td><a title="http://www.w3.org/ns/prov#hadUsage" href="#hadUsage" class="owlproperty">prov:hadUsage</a></td>
- <td>prov:wasUsedInDerivation</td>
- <td><a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlproperty">prov:Usage</a></td>
- </tr>
- <tr>
- <td></td>
- <td><a title="http://www.w3.org/ns/prov#influenced" href="#influenced" class="owlproperty">prov:influenced</a></td>
- <td>prov:wasInfluencedBy</td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlproperty">prov:Influence</a></td>
- <td><a title="http://www.w3.org/ns/prov#influencer" href="#influencer" class="owlproperty">prov:influencer</a></td>
- <td>prov:hadInfluence</td>
- <td>union</td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#invalidated" href="#invalidated" class="owlproperty">prov:invalidated</a></td>
- <td>prov:wasInvalidatedBy</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedAssociation" href="#qualifiedAssociation" class="owlproperty">prov:qualifiedAssociation</a></td>
- <td>prov:qualifiedAssociationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Association" href="#Association" class="owlproperty">prov:Association</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedAttribution" href="#qualifiedAttribution" class="owlproperty">prov:qualifiedAttribution</a></td>
- <td>prov:qualifiedAttributionOf</td>
- <td><a title="http://www.w3.org/ns/prov#Attribution" href="#Attribution" class="owlproperty">prov:Attribution</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedCommunication" href="#qualifiedCommunication" class="owlproperty">prov:qualifiedCommunication</a></td>
- <td>prov:qualifiedCommunicationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Communication" href="#Communication" class="owlproperty">prov:Communication</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlproperty">prov:Agent</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedDelegation" href="#qualifiedDelegation" class="owlproperty">prov:qualifiedDelegation</a></td>
- <td>prov:qualifiedDelegationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Delegation" href="#Delegation" class="owlproperty">prov:Delegation</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedDerivation" href="#qualifiedDerivation" class="owlproperty">prov:qualifiedDerivation</a></td>
- <td>prov:qualifiedDerivationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Derivation" href="#Derivation" class="owlproperty">prov:Derivation</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedEnd" href="#qualifiedEnd" class="owlproperty">prov:qualifiedEnd</a></td>
- <td>prov:qualifiedEndOf</td>
- <td><a title="http://www.w3.org/ns/prov#End" href="#End" class="owlproperty">prov:End</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedGeneration" href="#qualifiedGeneration" class="owlproperty">prov:qualifiedGeneration</a></td>
- <td>prov:qualifiedGenerationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Generation" href="#Generation" class="owlproperty">prov:Generation</a></td>
- </tr>
- <tr>
- <td>union</td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedInfluence" href="#qualifiedInfluence" class="owlproperty">prov:qualifiedInfluence</a></td>
- <td>prov:qualifiedInfluenceOf</td>
- <td><a title="http://www.w3.org/ns/prov#Influence" href="#Influence" class="owlproperty">prov:Influence</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedInvalidation" href="#qualifiedInvalidation" class="owlproperty">prov:qualifiedInvalidation</a></td>
- <td>prov:qualifiedInvalidationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Invalidation" href="#Invalidation" class="owlproperty">prov:Invalidation</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedPrimarySource" href="#qualifiedPrimarySource" class="owlproperty">prov:qualifiedPrimarySource</a></td>
- <td>prov:qualifiedSourceOf</td>
- <td><a title="http://www.w3.org/ns/prov#PrimarySource" href="#PrimarySource" class="owlproperty">prov:PrimarySource</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedQuotation" href="#qualifiedQuotation" class="owlproperty">prov:qualifiedQuotation</a></td>
- <td>prov:qualifiedQuotationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Quotation" href="#Quotation" class="owlproperty">prov:Quotation</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedRevision" href="#qualifiedRevision" class="owlproperty">prov:qualifiedRevision</a></td>
- <td>prov:revisedEntity</td>
- <td><a title="http://www.w3.org/ns/prov#Revision" href="#Revision" class="owlproperty">prov:Revision</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedStart" href="#qualifiedStart" class="owlproperty">prov:qualifiedStart</a></td>
- <td>prov:qualifiedStartOf</td>
- <td><a title="http://www.w3.org/ns/prov#Start" href="#Start" class="owlproperty">prov:Start</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#qualifiedUsage" href="#qualifiedUsage" class="owlproperty">prov:qualifiedUsage</a></td>
- <td>prov:qualifiedUsingActivity</td>
- <td><a title="http://www.w3.org/ns/prov#Usage" href="#Usage" class="owlproperty">prov:Usage</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#specializationOf" href="#specializationOf" class="owlproperty">prov:specializationOf</a></td>
- <td>prov:generalizationOf</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#used" href="#used" class="owlproperty">prov:used</a></td>
- <td>prov:wasUsedBy</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasAssociatedWith" href="#wasAssociatedWith" class="owlproperty">prov:wasAssociatedWith</a></td>
- <td>prov:wasAssociateFor</td>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlproperty">prov:Agent</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasAttributedTo" href="#wasAttributedTo" class="owlproperty">prov:wasAttributedTo</a></td>
- <td>prov:contributed</td>
- <td><a title="http://www.w3.org/ns/prov#Agent" href="#Agent" class="owlproperty">prov:Agent</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasDerivedFrom" href="#wasDerivedFrom" class="owlproperty">prov:wasDerivedFrom</a></td>
- <td>prov:hadDerivation</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasEndedBy" href="#wasEndedBy" class="owlproperty">prov:wasEndedBy</a></td>
- <td>prov:ended</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasGeneratedBy" href="#wasGeneratedBy" class="owlproperty">prov:wasGeneratedBy</a></td>
- <td>prov:generated</td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- </tr>
- <tr>
- <td>union</td>
- <td><a title="http://www.w3.org/ns/prov#wasInfluencedBy" href="#wasInfluencedBy" class="owlproperty">prov:wasInfluencedBy</a></td>
- <td>prov:influenced</td>
- <td>union</td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasInformedBy" href="#wasInformedBy" class="owlproperty">prov:wasInformedBy</a></td>
- <td>prov:informed</td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasInvalidatedBy" href="#wasInvalidatedBy" class="owlproperty">prov:wasInvalidatedBy</a></td>
- <td>prov:invalidated</td>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasQuotedFrom" href="#wasQuotedFrom" class="owlproperty">prov:wasQuotedFrom</a></td>
- <td>prov:quotedAs</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasRevisionOf" href="#wasRevisionOf" class="owlproperty">prov:wasRevisionOf</a></td>
- <td>prov:hadRevision</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
- <tr>
- <td><a title="http://www.w3.org/ns/prov#Activity" href="#Activity" class="owlproperty">prov:Activity</a></td>
- <td><a title="http://www.w3.org/ns/prov#wasStartedBy" href="#wasStartedBy" class="owlproperty">prov:wasStartedBy</a></td>
- <td>prov:started</td>
- <td><a title="http://www.w3.org/ns/prov#Entity" href="#Entity" class="owlproperty">prov:Entity</a></td>
- </tr>
-</table>
-</div>
-
-
-
-
- </div>
-
-
- <div class="appendix informative section" id="changes-since-wd-prov-o-20120724">
- <!--OddPage--><h2><span class="secno">C. </span>Changes since WD-prov-o-20120724</h2><p><em>This section is non-normative.</em></p>
- <ul>
- <li>Restated <a href="#hadRole" class="qname">prov:hadRole</a>'s domain to 'Association or InstantaneousEvent'
- instead of the original that enumerated the subclasses of InstantaneousEvent
- ('Association or End or Generation or Invalidation or Start or Usage').
- </li>
-
- <li>Renamed prov:Source to <a href="#PrimarySource" class="qname">prov:PrimarySource</a>
- and prov:qualifiedSource to <a href="#qualifiedPrimarySource" class="qname">prov:qualifiedPrimarySource</a>.
- </li>
-
- <li>Examples have been rewritten to avoid usage of TriG named
- graph syntax except for when showing bundles in
- prov:asInBundle and prov:mentionOf (since removed to a separate Note). A citation to TriG was added.
- </li>
-
- <li>Some examples have been elaborated to use resource names
- like <code>:illustration_usage</code> rather than
- <code>:usage_1</code>.
- </li>
-
- <li>Fixed naming mismatch by changing prov:hadOriginalSource to <a href="#hadPrimarySource" class="qname">prov:hadPrimarySource</a>.
-
- </li><li>Rephrased definitions for <a href="#EntityInfluence" class="qname">prov:EntityInfluence</a>,
- <a href="#ActivityInfluence" class="qname">prov:ActivityInfluence</a>, and <a href="#AgentInfluence" class="qname">prov:AgentInfluence</a>
- to align with the definition of their superclass <a href="#Influence" class="qname">prov:Influence</a>.
- </li>
-
- <li>Updated definitions for <a href="#Start" class="qname">prov:Start</a> and
- <a href="#End" class="qname">prov:End</a> from PROV-DM.
- </li>
-
- <li>The property chain for <a href="#wasInformedBy" class="qname">prov:wasInformedBy</a> was fixed from
- "qualifiedCommunication o entity subproperty of wasInformedBy"
- to "<a href="#qualifiedCommunication" class="qname">prov:qualifiedCommunication</a> o <a href="#p_activity" class="qname">prov:activity</a> subproperty of wasInformedBy"</li>
-
- <li>Removed prov:mentionOf and prov:asInBundle, which have been relocated to its own Note.</li>
-
- <li>Added comments encouraging the use of the more specific forms of <a href="#Influence" class="qname">prov:Influence</a>.</li>
-
- <li>Added uniform references to other "dated" PROV documents.</li>
-
- <li>Added <a href="#namespace-table">prefix namespace table</a>.</li>
-
- <li>Added <a href="#compliance">Compliance with this document</a> section.</li>
-
- <li>Corrected Turtle syntax for RL violations in <a href="#owl-profile">PROV-O OWL Profile</a> section. They were missing owl:unionOf.</li>
-
- <li>Updated attributions for the tools used to produce this document in <a href="#acknowledgements">Acknowledgements</a> section.</li>
-
- <li>Reworked the <a href="#description-expanded-terms">Expanded Terms</a> narrative and examples to better highlight each term.</li>
- </ul>
- </div>
-
-
- <div class="appendix informative section" id="changes-since-cr-prov-o-20121211">
- <!--OddPage--><h2><span class="secno">D. </span>Changes since CR-prov-o-20121211</h2><p><em>This section is non-normative.</em></p>
- <ul>
- <li>Updated exemplar in cross reference entry <a href="#hadGeneration" class="qname">prov:hadGeneration</a> to include <a href="#p_activity" class="qname">prov:activity</a> property.</li>
- <li>Reordered class and predicate terms from alphabetical to a more natural narrative-based order.</li>
- <li>Added <a href="#cross-reference-index">Term Index</a> to aid reading this document in printed form.</li>
- <li>Fixed typo 'iteself' to 'itself'.</li>
- <li>Removed inaccurate property characteristics (AsymmetricProperty, IrreflexiveProperty)
- in third example of <a href="#inverse-names">Appendix B</a>.</li>
- <li>Added note to <a href="#description-starting-point-terms">Starting Point Terms</a> stating that
- rdf:type and rdfs:label are used to express PROV-DM's prov:type and prov:label.</li>
- <li>Updated prov:value's out-of-date definition to conform to PROV-DM's (i.e., "Provides a value that is a direct representation of an entity.".</li>
- <li>Updated prov:wasDerivedFrom's out-of-date definition to conform to PROV-DM's
- (i.e., "A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.".</li>
- <li>Added xsd:dateType datatypes to exemplar in Invalidation and invalidatedAtTime.</li>
- <li>Fixed some incorrect wasAttributedTo/wasAssociatedWith in the cross reference exemplars.</li>
- <li> Changed the status of this document section: added new documents to the PROV Family of Document, and removed the how to read section, referring instead to PROV-OVERVIEW.
- <li> Changed all URLs to PROV documents.
- </ul>
- </div>
-
- <div class="appendix informative section" id="changes-since-pr-prov-o-20130312">
- <!--OddPage--><h2><span class="secno">E. </span>Changes since PR-prov-o-20130312</h2><p><em>This section is non-normative.</em></p>
- <ul>
- <li>Fixed typo in <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/#alternateOf">alternateOf</a> example: <tt>:london_forecast_043</tt> became <tt>:london_forecast_0413</tt></li>
- </ul>
- </div>
-
- <div class="appendix informative section" id="acknowledgements">
- <!--OddPage--><h2><span class="secno">F. </span>Acknowledgements</h2><p><em>This section is non-normative.</em></p>
-
- <p>This document has been produced by the PROV Working Group, and its contents reflect extensive discussion within the Working Group as a whole. The editors extend special thanks to Sandro Hawke (<acronym title="World Wide Web Consortium">W3C</acronym>/<acronym title="Massachusetts Institute of Technology">MIT</acronym>) and Ivan Herman (<acronym title="World Wide Web Consortium">W3C</acronym>/<acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym>), <acronym title="World Wide Web Consortium">W3C</acronym> contacts for the PROV Working Group.</p>
-
- <p> The editors acknowledge valuable contributions from the following:
- Tom Baker,
- David Booth,
- Robert Freimuth,
- Satrajit Ghosh,
- Ralph Hodgson,
- Renato Iannella,
- Jacek Kopecky,
- James Leigh,
- Jacco van Ossenbruggen,
- Alan Ruttenberg,
- Reza Samavi, and
- Antoine Zimmermann.
- </p>
-
- <p>Members of the PROV Working Group at the time of publication of this document were:
-
- Ilkay Altintas (Invited expert),
- Reza B'Far (Oracle Corporation),
- Khalid Belhajjame (University of Manchester),
- James Cheney (University of Edinburgh, School of Informatics),
- Sam Coppens (IBBT),
- David Corsar (University of Aberdeen, Computing Science),
- Stephen Cresswell (The National Archives),
- Tom De Nies (IBBT),
- Helena Deus (DERI Galway at the National University of Ireland, Galway, Ireland),
- Simon Dobson (Invited expert),
- Martin Doerr (Foundation for Research and Technology - Hellas(FORTH)),
- Kai Eckert (Invited expert),
- Jean-Pierre EVAIN (European Broadcasting Union, EBU-UER),
- James Frew (Invited expert),
- Irini Fundulaki (Foundation for Research and Technology - Hellas(FORTH)),
- Daniel Garijo (Universidad Politécnica de Madrid),
- Yolanda Gil (Invited expert),
- Ryan Golden (Oracle Corporation),
- Paul Groth (Vrije Universiteit),
- Olaf Hartig (Invited expert),
- David Hau (National Cancer Institute, NCI),
- Sandro Hawke (<acronym title="World Wide Web Consortium">W3C</acronym>/<acronym title="Massachusetts Institute of Technology">MIT</acronym>),
- Jörn Hees (German Research Center for Artificial Intelligence (DFKI) Gmbh),
- Ivan Herman, (<acronym title="World Wide Web Consortium">W3C</acronym>/<acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym>),
- Ralph Hodgson (TopQuadrant),
- Hook Hua (Invited expert),
- Trung Dong Huynh (University of Southampton),
- Graham Klyne (University of Oxford),
- Michael Lang (Revelytix, Inc.),
- Timothy Lebo (Rensselaer Polytechnic Institute),
- James McCusker (Rensselaer Polytechnic Institute),
- Deborah McGuinness (Rensselaer Polytechnic Institute),
- Simon Miles (Invited expert),
- Paolo Missier (School of Computing Science, Newcastle university),
- Luc Moreau (University of Southampton),
- James Myers (Rensselaer Polytechnic Institute),
- Vinh Nguyen (Wright State University),
- Edoardo Pignotti (University of Aberdeen, Computing Science),
- Paulo da Silva Pinheiro (Rensselaer Polytechnic Institute),
- Carl Reed (Open Geospatial Consortium),
- Adam Retter (Invited Expert),
- Christine Runnegar (Invited expert),
- Satya Sahoo (Invited expert),
- David Schaengold (Revelytix, Inc.),
- Daniel Schutzer (FSTC, Financial Services Technology Consortium),
- Yogesh Simmhan (Invited expert),
- Stian Soiland-Reyes (University of Manchester),
- Eric Stephan (Pacific Northwest National Laboratory),
- Linda Stewart (The National Archives),
- Ed Summers (Library of Congress),
- Maria Theodoridou (Foundation for Research and Technology - Hellas(FORTH)),
- Ted Thibodeau (OpenLink Software Inc.),
- Curt Tilmes (National Aeronautics and Space Administration),
- Craig Trim (IBM Corporation),
- Stephan Zednik (Rensselaer Polytechnic Institute),
- Jun Zhao (University of Oxford),
- Yuting Zhao (University of Aberdeen, Computing Science).
- </p>
-
- <p>The editors also thank the developers of the tools that helped create the PROV-O ontology and portions of this document. Without these great tools, developing PROV-O would have been much less of a pleasure.</p>
- <ul>
- <li>Stanford's <a href="http://protege.stanford.edu">Protege</a> for editing the ontology.</li>
- <li>Dave Beckett's <a href="http://librdf.org/raptor/">rapper</a> for the many serialization checks of so many examples.</li>
- <li>Cosmin Basca's <a href="http://packages.python.org/SuRF/">SuRF</a> for easing the construction of this page's cross reference section.</li>
- <li>The creators, contributors, and maintainers of <a href="https://github.com/RDFLib">rdflib</a> for easing the construction of this page's cross reference section.</li>
- <li>Alvaro Graves' <a href="http://alangrafu.github.com/lodspeakr/">LODSpeaKr</a> for constructing portions of this page with SPARQL queries of PROV-O.</li>
- <li>Silvio Peroni's <a href="http://lode.sourceforge.net">LODE</a> for the CSS styling of this page's cross reference section.</li>
- <li>Robin Berjon's <a href="http://dev.w3.org/2009/dap/ReSpec.js/documentation.html">respec</a> for handling the <acronym title="World Wide Web Consortium">W3C</acronym> styling.</li>
- </ul>
- </div>
-
-
-
-<div id="references" class="appendix section"><!--OddPage--><h2><span class="secno">G. </span>References</h2><div id="normative-references" class="section"><h3><span class="secno">G.1 </span>Normative references</h3><dl class="bibliography">
-
-<dt id="bib-IRI">[IRI]</dt>
-<dd>M. Duerst, M. Suignard. <a href="http://www.ietf.org/rfc/rfc3987.txt"><cite>Internationalized Resource Identifiers (IRI).</cite></a> January 2005. Internet RFC 3987. URL: <a href="http://www.ietf.org/rfc/rfc3986.txt">http://www.ietf.org/rfc/rfc3987.txt</a>
-</dd>
-
-<dt id="bib-OWL2-OVERVIEW">[OWL2-OVERVIEW]</dt><dd>W3C OWL Working Group. <a href="http://www.w3.org/TR/2009/REC-owl2-overview-20091027/"><cite>OWL 2 Web Ontology Language: Overview.</cite></a> 27 October 2009. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2009/REC-owl2-overview-20091027/">http://www.w3.org/TR/2009/REC-owl2-overview-20091027/</a>
-</dd>
-
-<dt id="bib-PROV-CONSTRAINTS">[PROV-CONSTRAINTS]</dt><dd>James Cheney; Paolo Missier; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/"><cite>Constraints of the PROV Data Model</cite></a>. 30 April 2013, W3C Recommendation. URL: <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/">http://www.w3.org/TR/2013/REC-prov-constraints-20130430/</a> </dd>
-
-<dt id="bib-PROV-DM">[PROV-DM]</dt>
-<dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/"><cite>PROV-DM: The PROV Data Model</cite></a>. 30 April 2013, W3C Recommendation. URL: <a href="http://www.w3.
-org/TR/2013/REC-prov-dm-20130430/">http://www.w3.org/TR/2013/REC-prov-dm-20130430/</a>
-</dd>
-
-
-<dt id="bib-PROV-N">[PROV-N]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2013/REC-prov-n-20130430/"><cite>PROV-N: The Provenance Notation</cite></a>. 30 April 2013, W3C Recommendation. URL: <a href="http://www.w3.org/TR/2013/REC-prov-n-20130430/">http://www.w3.org/TR/2013/REC-prov-n-20130430/</a> </dd>
-
-<dt id="bib-RDF-CONCEPTS">[RDF-CONCEPTS]</dt><dd>Graham Klyne; Jeremy J. Carroll. <a href="http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/"><cite>Resource Description Framework (RDF): Concepts and Abstract Syntax.</cite></a> 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/">http://www.w3.org/TR/2004/REC-rdf-concepts-20040210</a>
-</dd>
-
-<dt id="bib-RFC2119">[RFC2119]</dt><dd>S. Bradner. <a href="http://www.ietf.org/rfc/rfc2119.txt"><cite>Key words for use in RFCs to Indicate Requirement Levels.</cite></a> March 1997. Internet RFC 2119. URL: <a href="http://www.ietf.org/rfc/rfc2119.txt">http://www.ietf.org/rfc/rfc2119.txt</a>
-</dd>
-
-<dt id="bib-XMLSCHEMA11-2">[XMLSCHEMA11-2]</dt><dd>Henry S. Thompson; et al. <a href="http://www.w3.org/TR/2012/REC-xmlschema11-2-20120405/"><cite>W3C XML Schema Definition Language (XSD) 1.1 Part 2: Datatypes.</cite></a> 5 April 2012. W3C Recommendation URL: <a href="http://www.w3.org/TR/2012/REC-xmlschema11-2-20120405/">http://www.w3.org/TR/2012/REC-xmlschema11-2-20120405/</a>
-</dd></dl></div><div id="informative-references" class="section"><h3><span class="secno">G.2 </span>Informative references</h3><dl class="bibliography">
-
-<dt id="bib-LD-Patterns-QR">[LD-Patterns-QR]</dt><dd>Leigh Dodds; Ian Davis. <a href="http://patterns.dataincubator.org/book/qualified-relation.html"><cite>Qualified Relation</cite></a>. modified 31 May 2012, accessed 01 June 2012 URL: <a href="http://patterns.dataincubator.org/book/qualified-relation.html">http://patterns.dataincubator.org/book/qualified-relation.html</a>
-</dd>
-
-<dt id="bib-OWL2-PRIMER">[OWL2-PRIMER]</dt><dd>Pascal Hitzler; Markus Krötzsch; Bijan Parsia; Peter F. Patel-Schneider; Sebastian Rudolph. <a href="http://www.w3.org/TR/2009/REC-owl2-primer-20091027/"><cite>OWL 2 Web Ontology Language:Primer.</cite></a> 27 October 2009. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2009/REC-owl2-primer-20091027/">http://www.w3.org/TR/2009/REC-owl2-primer-20091027/</a>
-</dd>
-
-<dt id="bib-PROV-AQ">[PROV-AQ]</dt><dd>Graham Klyne; Paul Groth; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/"><cite>Provenance Access and Query</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/</a> </dd>
-
-
-<dt id="bib-PROV-DC">[PROV-DC]</dt><dd>Daniel Garijo; Kai Eckert; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/"><cite>Dublin Core to PROV Mapping</cite></a>. 30 April 2013, W3C Note. URL : <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/</a> </dd>
-
-
-
-<dt id="bib-PROV-DICTIONARY">[PROV-DICTIONARY]</dt><dd>Tom De Nies; Sam Coppens; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/"><cite>PROV Dictionary</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/</a> </dd>
-
-<dt id="bib-PROV-LINKS">[PROV-LINKS]</dt><dd>Luc Moreau; Timothy Lebo; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/"><cite>Linking Across Provenance Bundles</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">http://www.w3.org/TR/2013/NOTE-prov-links-20130430/</a> </dd>
-
-<dt id="bib-PROV-OVERVIEW">[PROV-OVERVIEW]</dt><dd>Paul Groth; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-overview-20130430/"><cite>PROV-OVERVIEW: An Overview of the PROV Family of Documents</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-overview-20130430/">http://www.w3.org/TR/2013/NOTE-prov-overview-20130430/</a> </dd>
-
-<dt id="bib-PROV-PRIMER">[PROV-PRIMER]</dt><dd>Yolanda Gil; Simon Miles; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-primer-20130430/"><cite>PROV Model Primer</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-primer-20130430/">http://www.w3.org/TR/2013/NOTE-prov-primer-20130430/</a> </dd>
-
-
-<dt id="bib-PROV-SEM">[PROV-SEM]</dt><dd>James Cheney; ed. <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430"><cite>Semantics of the PROV Data Model</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430">http://www.w3.org/TR/2013/NOTE-prov-sem-20130430</a>.
-</dd>
-
-
-
-<dt id="bib-PROV-XML">[PROV-XML]</dt><dd>Hook Hua; Curt Tilmes; Stephan Zednik; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/"><cite>PROV-XML: The PROV XML Schema</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/</a> </dd>
-
-
-<dt id="bib-RDF-SCHEMA">[RDF-SCHEMA]</dt><dd>Dan Brickley; Ramanathan V. Guha. <a href="http://www.w3.org/TR/2004/REC-rdf-schema-20040210/"><cite>RDF Vocabulary Description Language 1.0: RDF Schema.</cite></a> 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2004/REC-rdf-schema-20040210/">http://www.w3.org/TR/2004/REC-rdf-schema-20040210</a>
-</dd>
-
-<dt id="bib-TRIG">[TRIG]</dt><dd>Chris Bizer; Richard Cyganiak. <a href="http://wifo5-03.informatik.uni-mannheim.de/bizer/trig/"><cite>The TriG Syntax</cite></a>. modified 30 July 2007, accessed 05 November 2012 URL: <a href="http://wifo5-03.informatik.uni-mannheim.de/bizer/trig/">http://wifo5-03.informatik.uni-mannheim.de/bizer/trig/</a>
-</dd></dl></div></div></body></html>
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--- a/ontology/releases/FR-prov-o/ns/prov-o-20130312.owl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1788 +0,0 @@
-<?xml version="1.0"?>
-
-
-<!DOCTYPE rdf:RDF [
- <!ENTITY owl "http://www.w3.org/2002/07/owl#" >
- <!ENTITY xsd "http://www.w3.org/2001/XMLSchema#" >
- <!ENTITY rdfs "http://www.w3.org/2000/01/rdf-schema#" >
- <!ENTITY rdf "http://www.w3.org/1999/02/22-rdf-syntax-ns#" >
-]>
-
-
-<rdf:RDF xmlns="http://www.w3.org/ns/prov#"
- xml:base="http://www.w3.org/ns/prov"
- xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
- xmlns:owl="http://www.w3.org/2002/07/owl#"
- xmlns:xsd="http://www.w3.org/2001/XMLSchema#"
- xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
- <owl:Ontology rdf:about="http://www.w3.org/ns/prov-o#">
- <rdfs:label xml:lang="en">W3C PROVenance Interchange Ontology (PROV-O)</rdfs:label>
- <owl:versionInfo xml:lang="en">Proposed Recommendation version 2013-03-12</owl:versionInfo>
- <rdfs:comment xml:lang="en">This document is published by the Provenance Working Group (http://www.w3.org/2011/prov/wiki/Main_Page).
-
-If you wish to make comments regarding this document, please send them to public-prov-comments@w3.org (subscribe public-prov-comments-request@w3.org, archives http://lists.w3.org/Archives/Public/public-prov-comments/). All feedback is welcome.</rdfs:comment>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/TR/prov-o/"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov"/>
- <specializationOf rdf:resource="http://www.w3.org/ns/prov-o"/>
- <wasRevisionOf rdf:resource="http://www.w3.org/ns/prov-o-20121211"/>
- <owl:versionIRI rdf:resource="http://www.w3.org/ns/prov-o-20130312"/>
- </owl:Ontology>
-
- <owl:Ontology rdf:about="http://www.w3.org/ns/prov#"></owl:Ontology>
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Annotation properties
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#unqualifiedForm">
- <rdfs:comment xml:lang="en">Classes and properties used to qualify relationships are annotated with prov:unqualifiedForm to indicate the property used to assert an unqualified provenance relation.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#wasRevisionOf">
- <rdfs:label>wasRevisionOf</rdfs:label>
- <component>derivations</component>
- <rdfs:comment xml:lang="en">A revision is a derivation that revises an entity into a revised version.</rdfs:comment>
- <inverse>hadRevision</inverse>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedRevision"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#aq">
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#sharesDefinitionWith">
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#definition">
- <rdfs:comment xml:lang="en">A definition quoted from PROV-DM or PROV-CONSTRAINTS that describes the concept expressed with this OWL term.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#editorialNote">
- <rdfs:comment xml:lang="en">A note by the OWL development team about how this term expresses the PROV-DM concept, or how it should be used in context of semantic web or linked data.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&rdfs;label">
- <rdfs:comment xml:lang="en"></rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#inverse">
- <rdfs:comment xml:lang="en">PROV-O does not define all property inverses. The directionalities defined in PROV-O should be given preference over those not defined. However, if users wish to name the inverse of a PROV-O property, the local name given by prov:inverse should be used.</rdfs:comment>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/TR/prov-o/#names-of-inverse-properties"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&rdfs;comment">
- <rdfs:comment xml:lang="en"></rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#constraints">
- <rdfs:comment xml:lang="en">A reference to the principal section of the PROV-CONSTRAINTS document that describes this concept.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&owl;versionInfo"/>
- <owl:AnnotationProperty rdf:about="&rdfs;seeAlso">
- <rdfs:comment xml:lang="en"></rdfs:comment>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#specializationOf">
- <rdfs:label>specializationOf</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-specialization</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-specialization</n>
- <component>alternate</component>
- <inverse>generalizationOf</inverse>
- <category>expanded</category>
- <definition xml:lang="en">An entity that is a specialization of another shares all aspects of the latter, and additionally presents more specific aspects of the same thing as the latter. In particular, the lifetime of the entity being specialized contains that of any specialization. Examples of aspects include a time period, an abstraction, and a context associated with the entity.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#alternateOf"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#dm">
- <rdfs:comment xml:lang="en">A reference to the principal section of the PROV-DM document that describes this concept.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#category">
- <rdfs:comment xml:lang="en">Classify prov-o terms into three categories, including 'starting-point', 'qualifed', and 'extended'. This classification is used by the prov-o html document to gently introduce prov-o terms to its users. </rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#order">
- <rdfs:comment xml:lang="en">The position that this OWL term should be listed within documentation. The scope of the documentation (e.g., among all terms, among terms within a prov:category, among properties applying to a particular class, etc.) is unspecified.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&rdfs;isDefinedBy"/>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#editorsDefinition">
- <rdfs:comment xml:lang="en">When the prov-o term does not have a definition drawn from prov-dm, and the prov-o editor provides one.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#definition"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#component">
- <rdfs:comment xml:lang="en">Classify prov-o terms into six components according to prov-dm, including 'agents-responsibility', 'alternate', 'annotations', 'collections', 'derivations', and 'entities-activities'. This classification is used so that readers of prov-o specification can find its correspondence with the prov-dm specification.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#qualifiedForm">
- <rdfs:comment xml:lang="en">This annotation property links a subproperty of prov:wasInfluencedBy with the subclass of prov:Influence and the qualifying property that are used to qualify it.
-
-Example annotation:
-
- prov:wasGeneratedBy prov:qualifiedForm prov:qualifiedGeneration, prov:Generation .
-
-Then this unqualified assertion:
-
- :entity1 prov:wasGeneratedBy :activity1 .
-
-can be qualified by adding:
-
- :entity1 prov:qualifiedGeneration :entity1Gen .
- :entity1Gen
- a prov:Generation, prov:Influence;
- prov:activity :activity1;
- :customValue 1337 .
-
-Note how the value of the unqualified influence (prov:wasGeneratedBy :activity1) is mirrored as the value of the prov:activity (or prov:entity, or prov:agent) property on the influence class.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#todo"/>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#n">
- <rdfs:comment xml:lang="en">A reference to the principal section of the PROV-DM document that describes this concept.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Object Properties
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/ns/prov#actedOnBehalfOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#actedOnBehalfOf">
- <rdfs:label>actedOnBehalfOf</rdfs:label>
- <component>agents-responsibility</component>
- <inverse>hadDelegate</inverse>
- <rdfs:comment xml:lang="en">An object property to express the accountability of an agent towards another agent. The subordinate agent acted on behalf of the responsible agent in an actual activity. </rdfs:comment>
- <category>starting-point</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Delegation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedDelegation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedDelegation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#agent"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#activity -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#activity">
- <rdfs:label>activity</rdfs:label>
- <editorsDefinition>The prov:activity property references an prov:Activity which influenced a resource. This property applies to an prov:ActivityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</editorsDefinition>
- <inverse>activityOfInfluence</inverse>
- <editorialNote xml:lang="en">This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple.</editorialNote>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influencer"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#agent -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#agent">
- <rdfs:label>agent</rdfs:label>
- <editorsDefinition xml:lang="en">The prov:agent property references an prov:Agent which influenced a resource. This property applies to an prov:AgentInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</editorsDefinition>
- <inverse>agentOfInfluence</inverse>
- <editorialNote xml:lang="en">This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple.</editorialNote>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influencer"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#alternateOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#alternateOf">
- <rdfs:label>alternateOf</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-alternate</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-alternate</n>
- <definition xml:lang="en">Two alternate entities present aspects of the same thing. These aspects may be the same or different, and the alternate entities may or may not overlap in time.</definition>
- <category>expanded</category>
- <component>alternate</component>
- <inverse>alternateOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#specializationOf"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#atLocation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#atLocation">
- <rdfs:label>atLocation</rdfs:label>
- <rdfs:comment xml:lang="en">The Location of any resource.</rdfs:comment>
- <inverse>locationOf</inverse>
- <editorialNote xml:lang="en">The naming of prov:atLocation parallels prov:atTime, and is not named prov:hadLocation to avoid conflicting with the convention that prov:had* properties are used on prov:Influence classes.</editorialNote>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <editorialNote xml:lang="en">This property is not functional because the many values could be at a variety of granularies (In this building, in this room, in that chair).</editorialNote>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Location"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Location"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#entity -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#entity">
- <rdfs:label>entity</rdfs:label>
- <editorsDefinition>The prov:entity property references an prov:Entity which influenced a resource. This property applies to an prov:EntityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</editorsDefinition>
- <inverse>entityOfInfluence</inverse>
- <editorialNote xml:lang="en">This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple.</editorialNote>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influencer"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#generated -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#generated">
- <rdfs:label>generated</rdfs:label>
- <component>entities-activities</component>
- <inverse>wasGeneratedBy</inverse>
- <category>expanded</category>
- <editorialNote xml:lang="en">prov:generated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions.</editorialNote>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influenced"/>
- <owl:inverseOf rdf:resource="http://www.w3.org/ns/prov#wasGeneratedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadActivity -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadActivity">
- <rdfs:label>hadActivity</rdfs:label>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <rdfs:comment xml:lang="en">The _optional_ Activity of an Influence, which used, generated, invalidated, or was the responsibility of some Entity. This property is _not_ used by ActivityInfluence (use prov:activity instead).</rdfs:comment>
- <editorialNote xml:lang="en">The multiple rdfs:domain assertions are intended. One is simpler and works for OWL-RL, the union is more specific but is not recognized by OWL-RL.</editorialNote>
- <component>derivations</component>
- <category>qualified</category>
- <inverse>wasActivityOfInfluence</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Delegation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Derivation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#End"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Start"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadGeneration -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadGeneration">
- <rdfs:label>hadGeneration</rdfs:label>
- <inverse>generatedAsDerivation</inverse>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The _optional_ Generation involved in an Entity's Derivation.</rdfs:comment>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadMember -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadMember">
- <rdfs:label>hadMember</rdfs:label>
- <category>expanded</category>
- <component>expanded</component>
- <inverse>wasMemberOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Collection"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Collection"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment xml:lang="en">A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections.</rdfs:comment>
- <dm>http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection</dm>
- <owl:annotatedProperty rdf:resource="&rdfs;range"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#hadMember"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadPlan -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadPlan">
- <rdfs:label>hadPlan</rdfs:label>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <inverse>wasPlanOf</inverse>
- <rdfs:comment xml:lang="en">The _optional_ Plan adopted by an Agent in Association with some Activity. Plan specifications are out of the scope of this specification.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Plan"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Plan"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadPrimarySource -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadPrimarySource">
- <rdfs:label>hadPrimarySource</rdfs:label>
- <component>derivations</component>
- <category>expanded</category>
- <inverse>wasPrimarySourceOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#PrimarySource"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedPrimarySource"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedPrimarySource"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>hadPrimarySource property is a particular case of wasDerivedFrom (see http://www.w3.org/TR/prov-dm/#term-original-source) that aims to give credit to the source that originated some information.</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#hadPrimarySource"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadRole -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadRole">
- <rdfs:label>hadRole</rdfs:label>
- <component>agents-responsibility</component>
- <inverse>wasRoleIn</inverse>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The _optional_ Role that an Entity assumed in the context of an Activity. For example, :baking prov:used :spoon; prov:qualified [ a prov:Usage; prov:entity :spoon; prov:hadRole roles:mixing_implement ].</rdfs:comment>
- <editorsDefinition xml:lang="en">prov:hadRole references the Role (i.e. the function of an entity with respect to an activity), in the context of an instantaneous usage, generation, association, start, and end.</editorsDefinition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Role"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Role"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Association"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadUsage -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadUsage">
- <rdfs:label>hadUsage</rdfs:label>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The _optional_ Usage involved in an Entity's Derivation.</rdfs:comment>
- <inverse>wasUsedInDerivation</inverse>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#influenced -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#influenced">
- <rdfs:label>influenced</rdfs:label>
- <inverse>wasInfluencedBy</inverse>
- <component>agents-responsibility</component>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <owl:inverseOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#influencer -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#influencer">
- <rdfs:label>influencer</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <category>qualified</category>
- <inverse>hadInfluence</inverse>
- <rdfs:comment xml:lang="en">Subproperties of prov:influencer are used to cite the object of an unqualified PROV-O triple whose predicate is a subproperty of prov:wasInfluencedBy (e.g. prov:used, prov:wasGeneratedBy). prov:influencer is used much like rdf:object is used.</rdfs:comment>
- <editorialNote xml:lang="en">This property and its subproperties are used in the same way as the rdf:object property, i.e. to reference the object of an unqualified prov:wasInfluencedBy or prov:influenced triple.</editorialNote>
- <editorsDefinition xml:lang="en">This property is used as part of the qualified influence pattern. Subclasses of prov:Influence use these subproperties to reference the resource (Entity, Agent, or Activity) whose influence is being qualified.</editorsDefinition>
- <rdfs:range rdf:resource="&owl;Thing"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#invalidated -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#invalidated">
- <rdfs:label>invalidated</rdfs:label>
- <category>expanded</category>
- <inverse>wasInvalidatedBy</inverse>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">prov:invalidated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions.</editorialNote>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influenced"/>
- <owl:inverseOf rdf:resource="http://www.w3.org/ns/prov#wasInvalidatedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedAssociation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedAssociation">
- <rdfs:label>qualifiedAssociation</rdfs:label>
- <inverse>qualifiedAssociationOf</inverse>
- <rdfs:comment xml:lang="en">If this Activity prov:wasAssociatedWith Agent :ag, then it can qualify the Association using prov:qualifiedAssociation [ a prov:Association; prov:agent :ag; :foo :bar ].</rdfs:comment>
- <component>agents-responsibility</component>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAssociatedWith"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedAttribution -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedAttribution">
- <rdfs:label>qualifiedAttribution</rdfs:label>
- <inverse>qualifiedAttributionOf</inverse>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:comment xml:lang="en">If this Entity prov:wasAttributedTo Agent :ag, then it can qualify how it was influenced using prov:qualifiedAttribution [ a prov:Attribution; prov:agent :ag; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Attribution"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Attribution"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAttributedTo"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedCommunication -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedCommunication">
- <rdfs:label>qualifiedCommunication</rdfs:label>
- <inverse>qualifiedCommunicationOf</inverse>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:wasInformedBy Activity :a, then it can qualify how it was influenced using prov:qualifiedCommunication [ a prov:Communication; prov:activity :a; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedDelegation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedDelegation">
- <rdfs:label>qualifiedDelegation</rdfs:label>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">If this Agent prov:actedOnBehalfOf Agent :ag, then it can qualify how with prov:qualifiedResponsibility [ a prov:Responsibility; prov:agent :ag; :foo :bar ].</rdfs:comment>
- <inverse>qualifiedDelegationOf</inverse>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Delegation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Delegation"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#actedOnBehalfOf"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedDerivation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedDerivation">
- <rdfs:label>qualifiedDerivation</rdfs:label>
- <component>derivations</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">If this Entity prov:wasDerivedFrom Entity :e, then it can qualify how it was derived using prov:qualifiedDerivation [ a prov:Derivation; prov:entity :e; :foo :bar ].</rdfs:comment>
- <inverse>qualifiedDerivationOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedEnd -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedEnd">
- <rdfs:label>qualifiedEnd</rdfs:label>
- <category>qualified</category>
- <inverse>qualifiedEndOf</inverse>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:wasEndedBy Entity :e1, then it can qualify how it was ended using prov:qualifiedEnd [ a prov:End; prov:entity :e1; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#End"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#End"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasEndedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedGeneration -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedGeneration">
- <rdfs:label>qualifiedGeneration</rdfs:label>
- <inverse>qualifiedGenerationOf</inverse>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">If this Activity prov:generated Entity :e, then it can qualify how it performed the Generation using prov:qualifiedGeneration [ a prov:Generation; prov:entity :e; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasGeneratedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedInfluence -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedInfluence">
- <rdfs:label>qualifiedInfluence</rdfs:label>
- <rdfs:comment xml:lang="en">Because prov:qualifiedInfluence is a broad relation, the more specific relations (qualifiedCommunication, qualifiedDelegation, qualifiedEnd, etc.) should be used when applicable.</rdfs:comment>
- <category>qualified</category>
- <inverse>qualifiedInfluenceOf</inverse>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedInvalidation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedInvalidation">
- <rdfs:label>qualifiedInvalidation</rdfs:label>
- <rdfs:comment xml:lang="en">If this Entity prov:wasInvalidatedBy Activity :a, then it can qualify how it was invalidated using prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :a; :foo :bar ].</rdfs:comment>
- <component>entities-activities</component>
- <category>qualified</category>
- <inverse>qualifiedInvalidationOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInvalidatedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedPrimarySource -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedPrimarySource">
- <rdfs:label>qualifiedPrimarySource</rdfs:label>
- <rdfs:comment xml:lang="en">If this Entity prov:hadPrimarySource Entity :e, then it can qualify how using prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :e; :foo :bar ].</rdfs:comment>
- <component>derivations</component>
- <category>qualified</category>
- <inverse>qualifiedSourceOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#PrimarySource"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#PrimarySource"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#hadPrimarySource"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedQuotation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedQuotation">
- <rdfs:label>qualifiedQuotation</rdfs:label>
- <category>qualified</category>
- <inverse>qualifiedQuotationOf</inverse>
- <rdfs:comment xml:lang="en">If this Entity prov:wasQuotedFrom Entity :e, then it can qualify how using prov:qualifiedQuotation [ a prov:Quotation; prov:entity :e; :foo :bar ].</rdfs:comment>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Quotation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Quotation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasQuotedFrom"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedRevision -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedRevision">
- <rdfs:label>qualifiedRevision</rdfs:label>
- <rdfs:comment xml:lang="en">If this Entity prov:wasRevisionOf Entity :e, then it can qualify how it was revised using prov:qualifiedRevision [ a prov:Revision; prov:entity :e; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <inverse>revisedEntity</inverse>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasRevisionOf"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedStart -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedStart">
- <rdfs:label>qualifiedStart</rdfs:label>
- <inverse>qualifiedStartOf</inverse>
- <category>qualified</category>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:wasStartedBy Entity :e1, then it can qualify how it was started using prov:qualifiedStart [ a prov:Start; prov:entity :e1; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasStartedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedUsage -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedUsage">
- <rdfs:label>qualifiedUsage</rdfs:label>
- <category>qualified</category>
- <inverse>qualifiedUsingActivity</inverse>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:used Entity :e, then it can qualify how it used it using prov:qualifiedUsage [ a prov:Usage; prov:entity :e; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#used"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#specializationOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#specializationOf">
- <rdfs:label>specializationOf</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-specialization</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-specialization</n>
- <component>alternate</component>
- <category>expanded</category>
- <inverse>generalizationOf</inverse>
- <definition xml:lang="en">An entity that is a specialization of another shares all aspects of the latter, and additionally presents more specific aspects of the same thing as the latter. In particular, the lifetime of the entity being specialized contains that of any specialization. Examples of aspects include a time period, an abstraction, and a context associated with the entity.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#alternateOf"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#alternateOf"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#used -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#used">
- <rdfs:label>used</rdfs:label>
- <inverse>wasUsedBy</inverse>
- <rdfs:comment xml:lang="en">A prov:Entity that was used by this prov:Activity. For example, :baking prov:used :spoon, :egg, :oven .</rdfs:comment>
- <category>starting-point</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedUsage"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedUsage"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasAssociatedWith -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasAssociatedWith">
- <rdfs:label>wasAssociatedWith</rdfs:label>
- <component>agents-responsibility</component>
- <inverse>wasAssociateFor</inverse>
- <rdfs:comment xml:lang="en">An prov:Agent that had some (unspecified) responsibility for the occurrence of this prov:Activity.</rdfs:comment>
- <category>starting-point</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedAssociation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedAssociation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#agent"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasAttributedTo -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasAttributedTo">
- <rdfs:label>wasAttributedTo</rdfs:label>
- <component>agents-responsibility</component>
- <category>starting-point</category>
- <inverse>contributed</inverse>
- <definition xml:lang="en">Attribution is the ascribing of an entity to an agent.</definition>
- <rdfs:comment xml:lang="en">Attribution is the ascribing of an entity to an agent.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Attribution"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedAttribution"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedAttribution"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#agent"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <definition>IF wasAttributedTo(e2,ag1,aAttr) holds, THEN wasInfluencedBy(e2,ag1) also holds. </definition>
- <rdfs:comment>Attribution is a particular case of trace (see http://www.w3.org/TR/prov-dm/#concept-trace), in the sense that it links an entity to the agent that ascribed it.</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasAttributedTo"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasDerivedFrom -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasDerivedFrom">
- <rdfs:label>wasDerivedFrom</rdfs:label>
- <inverse>hadDerivation</inverse>
- <definition xml:lang="en">A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.</definition>
- <category>starting-point</category>
- <rdfs:comment xml:lang="en">The more specific subproperties of prov:wasDerivedFrom (i.e., prov:wasQuotedFrom, prov:wasRevisionOf, prov:hadPrimarySource) should be used when applicable.</rdfs:comment>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedDerivation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedDerivation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>Derivation is a particular case of trace (see http://www.w3.org/TR/prov-dm/#term-trace), since it links an entity to another entity that contributed to its existence.</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasEndedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasEndedBy">
- <rdfs:label>wasEndedBy</rdfs:label>
- <category>expanded</category>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">End is when an activity is deemed to have ended. An end may refer to an entity, known as trigger, that terminated the activity.</rdfs:comment>
- <inverse>ended</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#End"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedEnd"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedEnd"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasGeneratedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasGeneratedBy">
- <rdfs:label>wasGeneratedBy</rdfs:label>
- <inverse>generated</inverse>
- <category>starting-point</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedGeneration"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedGeneration"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#activity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasInfluencedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasInfluencedBy">
- <rdfs:label>wasInfluencedBy</rdfs:label>
- <rdfs:comment xml:lang="en">Because prov:wasInfluencedBy is a broad relation, its more specific subproperties (e.g. prov:wasInformedBy, prov:actedOnBehalfOf, prov:wasEndedBy, etc.) should be used when applicable.</rdfs:comment>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <editorialNote xml:lang="en">The sub-properties of prov:wasInfluencedBy can be elaborated in more detail using the Qualification Pattern. For example, the binary relation :baking prov:used :spoon can be qualified by asserting :baking prov:qualifiedUsage [ a prov:Usage; prov:entity :spoon; prov:atLocation :kitchen ] .
-
-Subproperties of prov:wasInfluencedBy may also be asserted directly without being qualified.
-
-prov:wasInfluencedBy should not be used without also using one of its subproperties.
-</editorialNote>
- <category>qualified</category>
- <inverse>influenced</inverse>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- <rdfs:range>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:range>
- </owl:ObjectProperty>
- <owl:Axiom>
- <definition>influencer: an identifier (o1) for an ancestor entity, activity, or agent that the former depends on;</definition>
- <dm>http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <owl:annotatedProperty rdf:resource="&rdfs;range"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:annotatedTarget>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </owl:annotatedTarget>
- </owl:Axiom>
- <owl:Axiom>
- <dm>http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <definition>influencee: an identifier (o2) for an entity, activity, or agent; </definition>
- <owl:annotatedProperty rdf:resource="&rdfs;domain"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:annotatedTarget>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </owl:annotatedTarget>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasInformedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasInformedBy">
- <rdfs:label>wasInformedBy</rdfs:label>
- <inverse>informed</inverse>
- <rdfs:comment xml:lang="en">An activity a2 is dependent on or informed by another activity a1, by way of some unspecified entity that is generated by a1 and used by a2.</rdfs:comment>
- <category>starting-point</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedCommunication"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedCommunication"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#activity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasInvalidatedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasInvalidatedBy">
- <rdfs:label>wasInvalidatedBy</rdfs:label>
- <component>entities-activities</component>
- <inverse>invalidated</inverse>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedInvalidation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedInvalidation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#activity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasQuotedFrom -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasQuotedFrom">
- <rdfs:label>wasQuotedFrom</rdfs:label>
- <category>expanded</category>
- <component>derivations</component>
- <inverse>quotedAs</inverse>
- <rdfs:comment xml:lang="en">An entity is derived from an original entity by copying, or 'quoting', some or all of it.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Quotation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedQuotation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedQuotation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>Quotation is a particular case of derivation (see http://www.w3.org/TR/prov-dm/#term-quotation) in which an entity is derived from an original entity by copying, or "quoting", some or all of it. </rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasQuotedFrom"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasRevisionOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasRevisionOf">
- <rdfs:label>wasRevisionOf</rdfs:label>
- <rdfs:comment xml:lang="en">A revision is a derivation that revises an entity into a revised version.</rdfs:comment>
- <component>derivations</component>
- <inverse>hadRevision</inverse>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedRevision"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedRevision"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>Revision is a derivation (see http://www.w3.org/TR/prov-dm/#term-Revision). Moreover, according to
-http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#term-Revision 23 April 2012 'wasRevisionOf is a strict sub-relation of wasDerivedFrom since two entities e2 and e1 may satisfy wasDerivedFrom(e2,e1) without being a variant of each other.'</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasRevisionOf"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasStartedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasStartedBy">
- <rdfs:label>wasStartedBy</rdfs:label>
- <inverse>started</inverse>
- <category>expanded</category>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">Start is when an activity is deemed to have started. A start may refer to an entity, known as trigger, that initiated the activity.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedStart"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedStart"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Data properties
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/ns/prov#atTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#atTime">
- <rdfs:label>atTime</rdfs:label>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The time at which an InstantaneousEvent occurred, in the form of xsd:dateTime.</rdfs:comment>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#endedAtTime"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#generatedAtTime"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#invalidatedAtTime"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#startedAtTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#endedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#endedAtTime">
- <rdfs:label>endedAtTime</rdfs:label>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedEnd o prov:atTime) rdfs:subPropertyOf prov:endedAtTime.</editorialNote>
- <rdfs:comment xml:lang="en">The time at which an activity ended. See also prov:startedAtTime.</rdfs:comment>
- <category>starting-point</category>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#End"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#generatedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#generatedAtTime">
- <rdfs:label>generatedAtTime</rdfs:label>
- <category>expanded</category>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedGeneration o prov:atTime) rdfs:subPropertyOf prov:generatedAtTime.</editorialNote>
- <rdfs:comment xml:lang="en">The time at which an entity was completely created and is available for use.</rdfs:comment>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#invalidatedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#invalidatedAtTime">
- <rdfs:label>invalidatedAtTime</rdfs:label>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedInvalidation o prov:atTime) rdfs:subPropertyOf prov:invalidatedAtTime.</editorialNote>
- <category>expanded</category>
- <rdfs:comment xml:lang="en">The time at which an entity was invalidated (i.e., no longer usable).</rdfs:comment>
- <component>entities-activities</component>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#startedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#startedAtTime">
- <rdfs:label>startedAtTime</rdfs:label>
- <category>starting-point</category>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedStart o prov:atTime) rdfs:subPropertyOf prov:startedAtTime.</editorialNote>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">The time at which an activity started. See also prov:endedAtTime.</rdfs:comment>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#value -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#value">
- <rdfs:label>value</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-value</dm>
- <category>expanded</category>
- <editorialNote>The editor's definition comes from http://www.w3.org/TR/rdf-primer/#rdfvalue</editorialNote>
- <definition xml:lang="en">Provides a value that is a direct representation of an entity.</definition>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">This property serves the same purpose as rdf:value, but has been reintroduced to avoid some of the definitional ambiguity in the RDF specification (specifically, 'may be used in describing structured values').</editorialNote>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- </owl:DatatypeProperty>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Classes
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/2002/07/owl#Thing -->
-
- <owl:Class rdf:about="&owl;Thing"/>
-
-
-
- <!-- http://www.w3.org/ns/prov#Activity -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Activity">
- <rdfs:label>Activity</rdfs:label>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Activity</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Activity</n>
- <component>entities-activities</component>
- <category>starting-point</category>
- <definition>An activity is something that occurs over a period of time and acts upon or with entities; it may include consuming, processing, transforming, modifying, relocating, using, or generating entities.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#ActivityInfluence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#ActivityInfluence">
- <rdfs:label>ActivityInfluence</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <rdfs:subClassOf>
- <owl:Restriction>
- <owl:onProperty rdf:resource="http://www.w3.org/ns/prov#hadActivity"/>
- <owl:maxCardinality rdf:datatype="&xsd;nonNegativeInteger">0</owl:maxCardinality>
- </owl:Restriction>
- </rdfs:subClassOf>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <editorsDefinition xml:lang="en">ActivitiyInfluence is the capacity of an activity to have an effect on the character, development, or behavior of another by means of generation, invalidation, communication, or other.</editorsDefinition>
- <rdfs:comment xml:lang="en">ActivityInfluence provides additional descriptions of an Activity's binary influence upon any other kind of resource. Instances of ActivityInfluence use the prov:activity property to cite the influencing Activity.</rdfs:comment>
- <rdfs:comment xml:lang="en">It is not recommended that the type ActivityInfluence be asserted without also asserting one of its more specific subclasses.</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#activity"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Agent -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Agent">
- <rdfs:label>Agent</rdfs:label>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Agent</n>
- <definition xml:lang="en">An agent is something that bears some form of responsibility for an activity taking place, for the existence of an entity, or for another agent's activity. </definition>
- <category>starting-point</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#AgentInfluence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#AgentInfluence">
- <rdfs:label>AgentInfluence</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <editorsDefinition xml:lang="en">AgentInfluence is the capacity of an agent to have an effect on the character, development, or behavior of another by means of attribution, association, delegation, or other.</editorsDefinition>
- <rdfs:comment xml:lang="en">AgentInfluence provides additional descriptions of an Agent's binary influence upon any other kind of resource. Instances of AgentInfluence use the prov:agent property to cite the influencing Agent.</rdfs:comment>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">It is not recommended that the type AgentInfluence be asserted without also asserting one of its more specific subclasses.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#agent"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Association -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Association">
- <rdfs:label>Association</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association</n>
- <component>agents-responsibility</component>
- <rdfs:comment xml:lang="en">An instance of prov:Association provides additional descriptions about the binary prov:wasAssociatedWith relation from an prov:Activity to some prov:Agent that had some responsiblity for it. For example, :baking prov:wasAssociatedWith :baker; prov:qualifiedAssociation [ a prov:Association; prov:agent :baker; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <definition xml:lang="en">An activity association is an assignment of responsibility to an agent for an activity, indicating that the agent had a role in the activity. It further allows for a plan to be specified, which is the plan intended by the agent to achieve some goals in the context of this activity.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAssociatedWith"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Attribution -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Attribution">
- <rdfs:label>Attribution</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribution</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribution</n>
- <rdfs:comment xml:lang="en">An instance of prov:Attribution provides additional descriptions about the binary prov:wasAttributedTo relation from an prov:Entity to some prov:Agent that had some responsible for it. For example, :cake prov:wasAttributedTo :baker; prov:qualifiedAttribution [ a prov:Attribution; prov:entity :baker; :foo :bar ].</rdfs:comment>
- <definition xml:lang="en">Attribution is the ascribing of an entity to an agent.
-
-When an entity e is attributed to agent ag, entity e was generated by some unspecified activity that in turn was associated to agent ag. Thus, this relation is useful when the activity is not known, or irrelevant.</definition>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAttributedTo"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Bundle -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Bundle">
- <rdfs:label>Bundle</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-bundle-entity</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-bundle-declaration</n>
- <category>expanded</category>
- <definition xml:lang="en">A bundle is a named set of provenance descriptions, and is itself an Entity, so allowing provenance of provenance to be expressed.</definition>
- <rdfs:comment xml:lang="en">Note that there are kinds of bundles (e.g. handwritten letters, audio recordings, etc.) that are not expressed in PROV-O, but can be still be described by PROV-O.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Collection -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Collection">
- <rdfs:label>Collection</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection</dm>
- <component>collections</component>
- <category>expanded</category>
- <definition xml:lang="en">A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Communication -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Communication">
- <rdfs:label>Communication</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Communication</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-wasInformedBy</n>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Communication provides additional descriptions about the binary prov:wasInformedBy relation from an informed prov:Activity to the prov:Activity that informed it. For example, :you_jumping_off_bridge prov:wasInformedBy :everyone_else_jumping_off_bridge; prov:qualifiedCommunication [ a prov:Communication; prov:activity :everyone_else_jumping_off_bridge; :foo :bar ].</rdfs:comment>
- <definition>Communication is the exchange of an entity by two activities, one activity using the entity generated by the other.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInformedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Delegation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Delegation">
- <rdfs:label>Delegation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-delegation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-delegation</n>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Delegation provides additional descriptions about the binary prov:actedOnBehalfOf relation from a performing prov:Agent to some prov:Agent for whom it was performed. For example, :mixing prov:wasAssociatedWith :toddler . :toddler prov:actedOnBehalfOf :mother; prov:qualifiedDelegation [ a prov:Delegation; prov:entity :mother; :foo :bar ].</rdfs:comment>
- <definition xml:lang="en">Delegation is the assignment of authority and responsibility to an agent (by itself or by another agent) to carry out a specific activity as a delegate or representative, while the agent it acts on behalf of retains some responsibility for the outcome of the delegated work.
-
-For example, a student acted on behalf of his supervisor, who acted on behalf of the department chair, who acted on behalf of the university; all those agents are responsible in some way for the activity that took place but we do not say explicitly who bears responsibility and to what degree.</definition>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#actedOnBehalfOf"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Derivation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Derivation">
- <rdfs:label>Derivation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Derivation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#Derivation-Relation</n>
- <definition xml:lang="en">A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.</definition>
- <component>derivations</component>
- <rdfs:comment xml:lang="en">An instance of prov:Derivation provides additional descriptions about the binary prov:wasDerivedFrom relation from some derived prov:Entity to another prov:Entity from which it was derived. For example, :chewed_bubble_gum prov:wasDerivedFrom :unwrapped_bubble_gum; prov:qualifiedDerivation [ a prov:Derivation; prov:entity :unwrapped_bubble_gum; :foo :bar ].</rdfs:comment>
- <rdfs:comment xml:lang="en">The more specific forms of prov:Derivation (i.e., prov:Revision, prov:Quotation, prov:PrimarySource) should be asserted if they apply.</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#EmptyCollection -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#EmptyCollection">
- <rdfs:label xml:lang="en">EmptyCollection</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Collection"/>
- <category>expanded</category>
- <component>collections</component>
- <definition xml:lang="en">An empty collection is a collection without members.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#End -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#End">
- <rdfs:label>End</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-End</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-End</n>
- <rdfs:comment xml:lang="en">An instance of prov:End provides additional descriptions about the binary prov:wasEndedBy relation from some ended prov:Activity to an prov:Entity that ended it. For example, :ball_game prov:wasEndedBy :buzzer; prov:qualifiedEnd [ a prov:End; prov:entity :buzzer; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ].</rdfs:comment>
- <category>qualified</category>
- <definition xml:lang="en">End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger.</definition>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasEndedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Entity -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Entity">
- <rdfs:label>Entity</rdfs:label>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-entity</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Entity</n>
- <component>entities-activities</component>
- <definition xml:lang="en">An entity is a physical, digital, conceptual, or other kind of thing with some fixed aspects; entities may be real or imaginary. </definition>
- <category>starting-point</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#EntityInfluence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#EntityInfluence">
- <rdfs:label>EntityInfluence</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <editorsDefinition xml:lang="en">EntityInfluence is the capacity of an entity to have an effect on the character, development, or behavior of another by means of usage, start, end, derivation, or other. </editorsDefinition>
- <rdfs:comment xml:lang="en">EntityInfluence provides additional descriptions of an Entity's binary influence upon any other kind of resource. Instances of EntityInfluence use the prov:entity property to cite the influencing Entity.</rdfs:comment>
- <rdfs:comment xml:lang="en">It is not recommended that the type EntityInfluence be asserted without also asserting one of its more specific subclasses.</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#entity"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Generation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Generation">
- <rdfs:label>Generation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Generation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Generation</n>
- <rdfs:comment xml:lang="en">An instance of prov:Generation provides additional descriptions about the binary prov:wasGeneratedBy relation from a generated prov:Entity to the prov:Activity that generated it. For example, :cake prov:wasGeneratedBy :baking; prov:qualifiedGeneration [ a prov:Generation; prov:activity :baking; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <component>entities-activities</component>
- <definition xml:lang="en">Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasGeneratedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Influence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Influence">
- <rdfs:label>Influence</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-influence</n>
- <component>derivations</component>
- <rdfs:comment xml:lang="en">An instance of prov:Influence provides additional descriptions about the binary prov:wasInfluencedBy relation from some influenced Activity, Entity, or Agent to the influencing Activity, Entity, or Agent. For example, :stomach_ache prov:wasInfluencedBy :spoon; prov:qualifiedInfluence [ a prov:Influence; prov:entity :spoon; :foo :bar ] . Because prov:Influence is a broad relation, the more specific relations (Communication, Delegation, End, etc.) should be used when applicable.</rdfs:comment>
- <rdfs:comment xml:lang="en">Because prov:Influence is a broad relation, its most specific subclasses (e.g. prov:Communication, prov:Delegation, prov:End, prov:Revision, etc.) should be used when applicable.</rdfs:comment>
- <category>qualified</category>
- <definition xml:lang="en">Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#InstantaneousEvent -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#InstantaneousEvent">
- <rdfs:label>InstantaneousEvent</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#dfn-event</constraints>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">An instantaneous event, or event for short, happens in the world and marks a change in the world, in its activities and in its entities. The term 'event' is commonly used in process algebra with a similar meaning. Events represent communications or interactions; they are assumed to be atomic and instantaneous.</rdfs:comment>
- <definition xml:lang="en">The PROV data model is implicitly based on a notion of instantaneous events (or just events), that mark transitions in the world. Events include generation, usage, or invalidation of entities, as well as starting or ending of activities. This notion of event is not first-class in the data model, but it is useful for explaining its other concepts and its semantics.</definition>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Invalidation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Invalidation">
- <rdfs:label>Invalidation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Invalidation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Invalidation</n>
- <component>entities-activities</component>
- <definition>Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation.</definition>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Invalidation provides additional descriptions about the binary prov:wasInvalidatedBy relation from an invalidated prov:Entity to the prov:Activity that invalidated it. For example, :uncracked_egg prov:wasInvalidatedBy :baking; prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :baking; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInvalidatedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Location -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Location">
- <rdfs:label>Location</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-location</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute</n>
- <definition xml:lang="en">A location can be an identifiable geographic place (ISO 19112), but it can also be a non-geographic place such as a directory, row, or column. As such, there are numerous ways in which location can be expressed, such as by a coordinate, address, landmark, and so forth.</definition>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#atLocation"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Organization -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Organization">
- <rdfs:label>Organization</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
- <definition>Agents of type Organization are social institutions such as companies, societies etc.</definition>
- <category>expanded</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Person -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Person">
- <rdfs:label>Person</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
- <category>expanded</category>
- <definition xml:lang="en">Agents of type Person are people.</definition>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Plan -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Plan">
- <rdfs:label>Plan</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association</n>
- <definition>A plan is an entity that represents a set of actions or steps intended by one or more agents to achieve some goals.</definition>
- <category>expanded</category>
- <rdfs:comment xml:lang="en">There exist no prescriptive requirement on the nature of plans, their representation, the actions or steps they consist of, or their intended goals. Since plans may evolve over time, it may become necessary to track their provenance, so plans themselves are entities. Representing the plan explicitly in the provenance can be useful for various tasks: for example, to validate the execution as represented in the provenance record, to manage expectation failures, or to provide explanations.</rdfs:comment>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#PrimarySource -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#PrimarySource">
- <rdfs:label>PrimarySource</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-primary-source</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-original-source</n>
- <category>qualified</category>
- <component>derivations</component>
- <definition xml:lang="en">A primary source for a topic refers to something produced by some agent with direct experience and knowledge about the topic, at the time of the topic's study, without benefit from hindsight.
-
-Because of the directness of primary sources, they 'speak for themselves' in ways that cannot be captured through the filter of secondary sources. As such, it is important for secondary sources to reference those primary sources from which they were derived, so that their reliability can be investigated.
-
-A primary source relation is a particular case of derivation of secondary materials from their primary sources. It is recognized that the determination of primary sources can be up to interpretation, and should be done according to conventions accepted within the application's domain.</definition>
- <rdfs:comment xml:lang="en">An instance of prov:PrimarySource provides additional descriptions about the binary prov:hadPrimarySource relation from some secondary prov:Entity to an earlier, primary prov:Entity. For example, :blog prov:hadPrimarySource :newsArticle; prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :newsArticle; :foo :bar ] .</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#hadPrimarySource"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Quotation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Quotation">
- <rdfs:label>Quotation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-quotation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-quotation</n>
- <rdfs:comment xml:lang="en">An instance of prov:Quotation provides additional descriptions about the binary prov:wasQuotedFrom relation from some taken prov:Entity from an earlier, larger prov:Entity. For example, :here_is_looking_at_you_kid prov:wasQuotedFrom :casablanca_script; prov:qualifiedQuotation [ a prov:Quotation; prov:entity :casablanca_script; :foo :bar ].</rdfs:comment>
- <component>derivations</component>
- <category>qualified</category>
- <definition xml:lang="en">A quotation is the repeat of (some or all of) an entity, such as text or image, by someone who may or may not be its original author. Quotation is a particular case of derivation.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasQuotedFrom"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Revision -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Revision">
- <rdfs:label>Revision</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-revision</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Revision</n>
- <component>derivations</component>
- <category>qualified</category>
- <definition xml:lang="en">A revision is a derivation for which the resulting entity is a revised version of some original. The implication here is that the resulting entity contains substantial content from the original. Revision is a particular case of derivation.</definition>
- <rdfs:comment xml:lang="en">An instance of prov:Revision provides additional descriptions about the binary prov:wasRevisionOf relation from some newer prov:Entity to an earlier prov:Entity. For example, :draft_2 prov:wasRevisionOf :draft_1; prov:qualifiedRevision [ a prov:Revision; prov:entity :draft_1; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasRevisionOf"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Role -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Role">
- <rdfs:label>Role</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-role</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute</n>
- <definition xml:lang="en">A role is the function of an entity or agent with respect to an activity, in the context of a usage, generation, invalidation, association, start, and end.</definition>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#hadRole"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#SoftwareAgent -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#SoftwareAgent">
- <rdfs:label>SoftwareAgent</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
- <component>agents-responsibility</component>
- <definition xml:lang="en">A software agent is running software.</definition>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Start -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Start">
- <rdfs:label>Start</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Start</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Start</n>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Start provides additional descriptions about the binary prov:wasStartedBy relation from some started prov:Activity to an prov:Entity that started it. For example, :foot_race prov:wasStartedBy :bang; prov:qualifiedStart [ a prov:Start; prov:entity :bang; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ] .</rdfs:comment>
- <definition xml:lang="en">Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasStartedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Usage -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Usage">
- <rdfs:label>Usage</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Usage</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Usage</n>
- <rdfs:comment xml:lang="en">An instance of prov:Usage provides additional descriptions about the binary prov:used relation from some prov:Activity to an prov:Entity that it used. For example, :keynote prov:used :podium; prov:qualifiedUsage [ a prov:Usage; prov:entity :podium; :foo :bar ].</rdfs:comment>
- <definition xml:lang="en">Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity.</definition>
- <category>qualified</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#used"/>
- </owl:Class>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Individuals
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/ns/prov#EmptyCollection -->
-
- <owl:NamedIndividual rdf:about="http://www.w3.org/ns/prov#EmptyCollection">
- <rdfs:label xml:lang="en">EmptyCollection</rdfs:label>
- <category>expanded</category>
- <component>collections</component>
- <definition xml:lang="en">An empty collection is a collection without members.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:NamedIndividual>
-</rdf:RDF>
-
-
-
-<!-- Generated by the OWL API (version 3.1.0.20069) http://owlapi.sourceforge.net -->
-
--- a/ontology/releases/FR-prov-o/ns/prov-o-20130312.ttl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1321 +0,0 @@
-@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
-@prefix : <http://www.w3.org/ns/prov#> .
-@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-
-rdfs:comment
- a owl:AnnotationProperty ;
- rdfs:comment ""@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-rdfs:isDefinedBy
- a owl:AnnotationProperty .
-
-rdfs:label
- a owl:AnnotationProperty ;
- rdfs:comment ""@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-rdfs:seeAlso
- a owl:AnnotationProperty ;
- rdfs:comment ""@en .
-
-owl:Thing
- a owl:Class .
-
-owl:versionInfo
- a owl:AnnotationProperty .
-
-<http://www.w3.org/ns/prov#>
- a owl:Ontology .
-
-:Activity
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Activity" ;
- owl:disjointWith :Entity ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "An activity is something that occurs over a period of time and acts upon or with entities; it may include consuming, processing, transforming, modifying, relocating, using, or generating entities." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Activity"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Activity"^^xsd:anyURI .
-
-:ActivityInfluence
- a owl:Class ;
- rdfs:comment "ActivityInfluence provides additional descriptions of an Activity's binary influence upon any other kind of resource. Instances of ActivityInfluence use the prov:activity property to cite the influencing Activity."@en, "It is not recommended that the type ActivityInfluence be asserted without also asserting one of its more specific subclasses."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "ActivityInfluence" ;
- rdfs:seeAlso :activity ;
- rdfs:subClassOf :Influence, [
- a owl:Restriction ;
- owl:maxCardinality "0"^^xsd:nonNegativeInteger ;
- owl:onProperty :hadActivity
- ] ;
- owl:disjointWith :EntityInfluence ;
- :category "qualified" ;
- :editorsDefinition "ActivitiyInfluence is the capacity of an activity to have an effect on the character, development, or behavior of another by means of generation, invalidation, communication, or other."@en .
-
-:Agent
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Agent" ;
- owl:disjointWith :InstantaneousEvent ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :definition "An agent is something that bears some form of responsibility for an activity taking place, for the existence of an entity, or for another agent's activity. "@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Agent"^^xsd:anyURI .
-
-:AgentInfluence
- a owl:Class ;
- rdfs:comment "AgentInfluence provides additional descriptions of an Agent's binary influence upon any other kind of resource. Instances of AgentInfluence use the prov:agent property to cite the influencing Agent."@en, "It is not recommended that the type AgentInfluence be asserted without also asserting one of its more specific subclasses."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "AgentInfluence" ;
- rdfs:seeAlso :agent ;
- rdfs:subClassOf :Influence ;
- :category "qualified" ;
- :editorsDefinition "AgentInfluence is the capacity of an agent to have an effect on the character, development, or behavior of another by means of attribution, association, delegation, or other."@en .
-
-:Association
- a owl:Class ;
- rdfs:comment "An instance of prov:Association provides additional descriptions about the binary prov:wasAssociatedWith relation from an prov:Activity to some prov:Agent that had some responsiblity for it. For example, :baking prov:wasAssociatedWith :baker; prov:qualifiedAssociation [ a prov:Association; prov:agent :baker; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Association" ;
- rdfs:subClassOf :AgentInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :definition "An activity association is an assignment of responsibility to an agent for an activity, indicating that the agent had a role in the activity. It further allows for a plan to be specified, which is the plan intended by the agent to achieve some goals in the context of this activity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association"^^xsd:anyURI ;
- :unqualifiedForm :wasAssociatedWith .
-
-:Attribution
- a owl:Class ;
- rdfs:comment "An instance of prov:Attribution provides additional descriptions about the binary prov:wasAttributedTo relation from an prov:Entity to some prov:Agent that had some responsible for it. For example, :cake prov:wasAttributedTo :baker; prov:qualifiedAttribution [ a prov:Attribution; prov:entity :baker; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Attribution" ;
- rdfs:subClassOf :AgentInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition """Attribution is the ascribing of an entity to an agent.
-
-When an entity e is attributed to agent ag, entity e was generated by some unspecified activity that in turn was associated to agent ag. Thus, this relation is useful when the activity is not known, or irrelevant."""@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribution"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribution"^^xsd:anyURI ;
- :unqualifiedForm :wasAttributedTo .
-
-:Bundle
- a owl:Class ;
- rdfs:comment "Note that there are kinds of bundles (e.g. handwritten letters, audio recordings, etc.) that are not expressed in PROV-O, but can be still be described by PROV-O."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Bundle" ;
- rdfs:subClassOf :Entity ;
- :category "expanded" ;
- :definition "A bundle is a named set of provenance descriptions, and is itself an Entity, so allowing provenance of provenance to be expressed."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-bundle-entity"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-bundle-declaration"^^xsd:anyURI .
-
-:Collection
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Collection" ;
- rdfs:subClassOf :Entity ;
- :category "expanded" ;
- :component "collections" ;
- :definition "A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection"^^xsd:anyURI .
-
-:Communication
- a owl:Class ;
- rdfs:comment "An instance of prov:Communication provides additional descriptions about the binary prov:wasInformedBy relation from an informed prov:Activity to the prov:Activity that informed it. For example, :you_jumping_off_bridge prov:wasInformedBy :everyone_else_jumping_off_bridge; prov:qualifiedCommunication [ a prov:Communication; prov:activity :everyone_else_jumping_off_bridge; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Communication" ;
- rdfs:subClassOf :ActivityInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Communication is the exchange of an entity by two activities, one activity using the entity generated by the other." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Communication"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-wasInformedBy"^^xsd:anyURI ;
- :unqualifiedForm :wasInformedBy .
-
-:Delegation
- a owl:Class ;
- rdfs:comment "An instance of prov:Delegation provides additional descriptions about the binary prov:actedOnBehalfOf relation from a performing prov:Agent to some prov:Agent for whom it was performed. For example, :mixing prov:wasAssociatedWith :toddler . :toddler prov:actedOnBehalfOf :mother; prov:qualifiedDelegation [ a prov:Delegation; prov:entity :mother; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Delegation" ;
- rdfs:subClassOf :AgentInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :definition """Delegation is the assignment of authority and responsibility to an agent (by itself or by another agent) to carry out a specific activity as a delegate or representative, while the agent it acts on behalf of retains some responsibility for the outcome of the delegated work.
-
-For example, a student acted on behalf of his supervisor, who acted on behalf of the department chair, who acted on behalf of the university; all those agents are responsible in some way for the activity that took place but we do not say explicitly who bears responsibility and to what degree."""@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-delegation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-delegation"^^xsd:anyURI ;
- :unqualifiedForm :actedOnBehalfOf .
-
-:Derivation
- a owl:Class ;
- rdfs:comment "An instance of prov:Derivation provides additional descriptions about the binary prov:wasDerivedFrom relation from some derived prov:Entity to another prov:Entity from which it was derived. For example, :chewed_bubble_gum prov:wasDerivedFrom :unwrapped_bubble_gum; prov:qualifiedDerivation [ a prov:Derivation; prov:entity :unwrapped_bubble_gum; :foo :bar ]."@en, "The more specific forms of prov:Derivation (i.e., prov:Revision, prov:Quotation, prov:PrimarySource) should be asserted if they apply."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Derivation" ;
- rdfs:subClassOf :EntityInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Derivation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#Derivation-Relation"^^xsd:anyURI ;
- :unqualifiedForm :wasDerivedFrom .
-
-:EmptyCollection
- a owl:Class, owl:NamedIndividual ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "EmptyCollection"@en ;
- rdfs:subClassOf :Collection ;
- :category "expanded" ;
- :component "collections" ;
- :definition "An empty collection is a collection without members."@en .
-
-:End
- a owl:Class ;
- rdfs:comment "An instance of prov:End provides additional descriptions about the binary prov:wasEndedBy relation from some ended prov:Activity to an prov:Entity that ended it. For example, :ball_game prov:wasEndedBy :buzzer; prov:qualifiedEnd [ a prov:End; prov:entity :buzzer; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "End" ;
- rdfs:subClassOf :EntityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-End"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-End"^^xsd:anyURI ;
- :unqualifiedForm :wasEndedBy .
-
-:Entity
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Entity" ;
- owl:disjointWith :InstantaneousEvent ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "An entity is a physical, digital, conceptual, or other kind of thing with some fixed aspects; entities may be real or imaginary. "@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-entity"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Entity"^^xsd:anyURI .
-
-:EntityInfluence
- a owl:Class ;
- rdfs:comment "EntityInfluence provides additional descriptions of an Entity's binary influence upon any other kind of resource. Instances of EntityInfluence use the prov:entity property to cite the influencing Entity."@en, "It is not recommended that the type EntityInfluence be asserted without also asserting one of its more specific subclasses."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "EntityInfluence" ;
- rdfs:seeAlso :entity ;
- rdfs:subClassOf :Influence ;
- :category "qualified" ;
- :editorsDefinition "EntityInfluence is the capacity of an entity to have an effect on the character, development, or behavior of another by means of usage, start, end, derivation, or other. "@en .
-
-:Generation
- a owl:Class ;
- rdfs:comment "An instance of prov:Generation provides additional descriptions about the binary prov:wasGeneratedBy relation from a generated prov:Entity to the prov:Activity that generated it. For example, :cake prov:wasGeneratedBy :baking; prov:qualifiedGeneration [ a prov:Generation; prov:activity :baking; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Generation" ;
- rdfs:subClassOf :ActivityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Generation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Generation"^^xsd:anyURI ;
- :unqualifiedForm :wasGeneratedBy .
-
-:Influence
- a owl:Class ;
- rdfs:comment "An instance of prov:Influence provides additional descriptions about the binary prov:wasInfluencedBy relation from some influenced Activity, Entity, or Agent to the influencing Activity, Entity, or Agent. For example, :stomach_ache prov:wasInfluencedBy :spoon; prov:qualifiedInfluence [ a prov:Influence; prov:entity :spoon; :foo :bar ] . Because prov:Influence is a broad relation, the more specific relations (Communication, Delegation, End, etc.) should be used when applicable."@en, "Because prov:Influence is a broad relation, its most specific subclasses (e.g. prov:Communication, prov:Delegation, prov:End, prov:Revision, etc.) should be used when applicable."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Influence" ;
- :category "qualified" ;
- :component "derivations" ;
- :definition "Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-influence"^^xsd:anyURI ;
- :unqualifiedForm :wasInfluencedBy .
-
-:InstantaneousEvent
- a owl:Class ;
- rdfs:comment "An instantaneous event, or event for short, happens in the world and marks a change in the world, in its activities and in its entities. The term 'event' is commonly used in process algebra with a similar meaning. Events represent communications or interactions; they are assumed to be atomic and instantaneous."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "InstantaneousEvent" ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#dfn-event"^^xsd:anyURI ;
- :definition "The PROV data model is implicitly based on a notion of instantaneous events (or just events), that mark transitions in the world. Events include generation, usage, or invalidation of entities, as well as starting or ending of activities. This notion of event is not first-class in the data model, but it is useful for explaining its other concepts and its semantics."@en .
-
-:Invalidation
- a owl:Class ;
- rdfs:comment "An instance of prov:Invalidation provides additional descriptions about the binary prov:wasInvalidatedBy relation from an invalidated prov:Entity to the prov:Activity that invalidated it. For example, :uncracked_egg prov:wasInvalidatedBy :baking; prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :baking; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Invalidation" ;
- rdfs:subClassOf :ActivityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Invalidation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Invalidation"^^xsd:anyURI ;
- :unqualifiedForm :wasInvalidatedBy .
-
-:Location
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Location" ;
- rdfs:seeAlso :atLocation ;
- :category "expanded" ;
- :definition "A location can be an identifiable geographic place (ISO 19112), but it can also be a non-geographic place such as a directory, row, or column. As such, there are numerous ways in which location can be expressed, such as by a coordinate, address, landmark, and so forth."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-location"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute"^^xsd:anyURI .
-
-:Organization
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Organization" ;
- rdfs:subClassOf :Agent ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :definition "Agents of type Organization are social institutions such as companies, societies etc." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types"^^xsd:anyURI .
-
-:Person
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Person" ;
- rdfs:subClassOf :Agent ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :definition "Agents of type Person are people."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types"^^xsd:anyURI .
-
-:Plan
- a owl:Class ;
- rdfs:comment "There exist no prescriptive requirement on the nature of plans, their representation, the actions or steps they consist of, or their intended goals. Since plans may evolve over time, it may become necessary to track their provenance, so plans themselves are entities. Representing the plan explicitly in the provenance can be useful for various tasks: for example, to validate the execution as represented in the provenance record, to manage expectation failures, or to provide explanations."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Plan" ;
- rdfs:subClassOf :Entity ;
- :category "expanded", "qualified" ;
- :component "agents-responsibility" ;
- :definition "A plan is an entity that represents a set of actions or steps intended by one or more agents to achieve some goals." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association"^^xsd:anyURI .
-
-:PrimarySource
- a owl:Class ;
- rdfs:comment "An instance of prov:PrimarySource provides additional descriptions about the binary prov:hadPrimarySource relation from some secondary prov:Entity to an earlier, primary prov:Entity. For example, :blog prov:hadPrimarySource :newsArticle; prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :newsArticle; :foo :bar ] ."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "PrimarySource" ;
- rdfs:subClassOf :Derivation ;
- :category "qualified" ;
- :component "derivations" ;
- :definition """A primary source for a topic refers to something produced by some agent with direct experience and knowledge about the topic, at the time of the topic's study, without benefit from hindsight.
-
-Because of the directness of primary sources, they 'speak for themselves' in ways that cannot be captured through the filter of secondary sources. As such, it is important for secondary sources to reference those primary sources from which they were derived, so that their reliability can be investigated.
-
-A primary source relation is a particular case of derivation of secondary materials from their primary sources. It is recognized that the determination of primary sources can be up to interpretation, and should be done according to conventions accepted within the application's domain."""@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-primary-source"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-original-source"^^xsd:anyURI ;
- :unqualifiedForm :hadPrimarySource .
-
-:Quotation
- a owl:Class ;
- rdfs:comment "An instance of prov:Quotation provides additional descriptions about the binary prov:wasQuotedFrom relation from some taken prov:Entity from an earlier, larger prov:Entity. For example, :here_is_looking_at_you_kid prov:wasQuotedFrom :casablanca_script; prov:qualifiedQuotation [ a prov:Quotation; prov:entity :casablanca_script; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Quotation" ;
- rdfs:subClassOf :Derivation ;
- :category "qualified" ;
- :component "derivations" ;
- :definition "A quotation is the repeat of (some or all of) an entity, such as text or image, by someone who may or may not be its original author. Quotation is a particular case of derivation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-quotation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-quotation"^^xsd:anyURI ;
- :unqualifiedForm :wasQuotedFrom .
-
-:Revision
- a owl:Class ;
- rdfs:comment "An instance of prov:Revision provides additional descriptions about the binary prov:wasRevisionOf relation from some newer prov:Entity to an earlier prov:Entity. For example, :draft_2 prov:wasRevisionOf :draft_1; prov:qualifiedRevision [ a prov:Revision; prov:entity :draft_1; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Revision" ;
- rdfs:subClassOf :Derivation ;
- :category "qualified" ;
- :component "derivations" ;
- :definition "A revision is a derivation for which the resulting entity is a revised version of some original. The implication here is that the resulting entity contains substantial content from the original. Revision is a particular case of derivation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-revision"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Revision"^^xsd:anyURI ;
- :unqualifiedForm :wasRevisionOf .
-
-:Role
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Role" ;
- rdfs:seeAlso :hadRole ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :definition "A role is the function of an entity or agent with respect to an activity, in the context of a usage, generation, invalidation, association, start, and end."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-role"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute"^^xsd:anyURI .
-
-:SoftwareAgent
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "SoftwareAgent" ;
- rdfs:subClassOf :Agent ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :definition "A software agent is running software."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types"^^xsd:anyURI .
-
-:Start
- a owl:Class ;
- rdfs:comment "An instance of prov:Start provides additional descriptions about the binary prov:wasStartedBy relation from some started prov:Activity to an prov:Entity that started it. For example, :foot_race prov:wasStartedBy :bang; prov:qualifiedStart [ a prov:Start; prov:entity :bang; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ] ."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Start" ;
- rdfs:subClassOf :EntityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Start"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Start"^^xsd:anyURI ;
- :unqualifiedForm :wasStartedBy .
-
-:Usage
- a owl:Class ;
- rdfs:comment "An instance of prov:Usage provides additional descriptions about the binary prov:used relation from some prov:Activity to an prov:Entity that it used. For example, :keynote prov:used :podium; prov:qualifiedUsage [ a prov:Usage; prov:entity :podium; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Usage" ;
- rdfs:subClassOf :EntityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Usage"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Usage"^^xsd:anyURI ;
- :unqualifiedForm :used .
-
-:actedOnBehalfOf
- a owl:ObjectProperty ;
- rdfs:comment "An object property to express the accountability of an agent towards another agent. The subordinate agent acted on behalf of the responsible agent in an actual activity. "@en ;
- rdfs:domain :Agent ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "actedOnBehalfOf" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedDelegation
- :agent
- ) ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :inverse "hadDelegate" ;
- :qualifiedForm :Delegation, :qualifiedDelegation .
-
-:activity
- a owl:ObjectProperty ;
- rdfs:domain :ActivityInfluence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "activity" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :influencer ;
- :category "qualified" ;
- :editorialNote "This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple."@en ;
- :editorsDefinition "The prov:activity property references an prov:Activity which influenced a resource. This property applies to an prov:ActivityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent." ;
- :inverse "activityOfInfluence" .
-
-:agent
- a owl:ObjectProperty ;
- rdfs:domain :AgentInfluence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "agent" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :influencer ;
- :category "qualified" ;
- :editorialNote "This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple."@en ;
- :editorsDefinition "The prov:agent property references an prov:Agent which influenced a resource. This property applies to an prov:AgentInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent."@en ;
- :inverse "agentOfInfluence" .
-
-:alternateOf
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "alternateOf" ;
- rdfs:range :Entity ;
- rdfs:seeAlso :specializationOf ;
- :category "expanded" ;
- :component "alternate" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Two alternate entities present aspects of the same thing. These aspects may be the same or different, and the alternate entities may or may not overlap in time."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-alternate"^^xsd:anyURI ;
- :inverse "alternateOf" ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-alternate"^^xsd:anyURI .
-
-:aq
- a owl:AnnotationProperty ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:atLocation
- a owl:ObjectProperty ;
- rdfs:comment "The Location of any resource."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- :InstantaneousEvent
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "atLocation" ;
- rdfs:range :Location ;
- :category "expanded" ;
- :editorialNote "The naming of prov:atLocation parallels prov:atTime, and is not named prov:hadLocation to avoid conflicting with the convention that prov:had* properties are used on prov:Influence classes."@en, "This property is not functional because the many values could be at a variety of granularies (In this building, in this room, in that chair)."@en ;
- :inverse "locationOf" ;
- :sharesDefinitionWith :Location .
-
-:atTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an InstantaneousEvent occurred, in the form of xsd:dateTime."@en ;
- rdfs:domain :InstantaneousEvent ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "atTime" ;
- rdfs:range xsd:dateTime ;
- :category "qualified" ;
- :component "entities-activities" ;
- :sharesDefinitionWith :InstantaneousEvent ;
- :unqualifiedForm :endedAtTime, :generatedAtTime, :invalidatedAtTime, :startedAtTime .
-
-:category
- a owl:AnnotationProperty ;
- rdfs:comment "Classify prov-o terms into three categories, including 'starting-point', 'qualifed', and 'extended'. This classification is used by the prov-o html document to gently introduce prov-o terms to its users. "@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:component
- a owl:AnnotationProperty ;
- rdfs:comment "Classify prov-o terms into six components according to prov-dm, including 'agents-responsibility', 'alternate', 'annotations', 'collections', 'derivations', and 'entities-activities'. This classification is used so that readers of prov-o specification can find its correspondence with the prov-dm specification."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:constraints
- a owl:AnnotationProperty ;
- rdfs:comment "A reference to the principal section of the PROV-CONSTRAINTS document that describes this concept."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:definition
- a owl:AnnotationProperty ;
- rdfs:comment "A definition quoted from PROV-DM or PROV-CONSTRAINTS that describes the concept expressed with this OWL term."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:dm
- a owl:AnnotationProperty ;
- rdfs:comment "A reference to the principal section of the PROV-DM document that describes this concept."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:editorialNote
- a owl:AnnotationProperty ;
- rdfs:comment "A note by the OWL development team about how this term expresses the PROV-DM concept, or how it should be used in context of semantic web or linked data."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:editorsDefinition
- a owl:AnnotationProperty ;
- rdfs:comment "When the prov-o term does not have a definition drawn from prov-dm, and the prov-o editor provides one."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf :definition .
-
-:endedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an activity ended. See also prov:startedAtTime."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "endedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedEnd o prov:atTime) rdfs:subPropertyOf prov:endedAtTime."@en ;
- :qualifiedForm :End, :atTime .
-
-:entity
- a owl:ObjectProperty ;
- rdfs:domain :EntityInfluence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "entity" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :influencer ;
- :category "qualified" ;
- :editorialNote "This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple."@en ;
- :editorsDefinition "The prov:entity property references an prov:Entity which influenced a resource. This property applies to an prov:EntityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent." ;
- :inverse "entityOfInfluence" .
-
-:generated
- a owl:ObjectProperty ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "generated" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :influenced ;
- owl:inverseOf :wasGeneratedBy ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "prov:generated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions."@en ;
- :inverse "wasGeneratedBy" ;
- :sharesDefinitionWith :Generation .
-
-:generatedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an entity was completely created and is available for use."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "generatedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedGeneration o prov:atTime) rdfs:subPropertyOf prov:generatedAtTime."@en ;
- :qualifiedForm :Generation, :atTime .
-
-:hadActivity
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Activity of an Influence, which used, generated, invalidated, or was the responsibility of some Entity. This property is _not_ used by ActivityInfluence (use prov:activity instead)."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain :Influence, [
- a owl:Class ;
- owl:unionOf (:Delegation
- :Derivation
- :End
- :Start
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadActivity" ;
- rdfs:range :Activity ;
- :category "qualified" ;
- :component "derivations" ;
- :editorialNote "The multiple rdfs:domain assertions are intended. One is simpler and works for OWL-RL, the union is more specific but is not recognized by OWL-RL."@en ;
- :inverse "wasActivityOfInfluence" ;
- :sharesDefinitionWith :Activity .
-
-:hadGeneration
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Generation involved in an Entity's Derivation."@en ;
- rdfs:domain :Derivation ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadGeneration" ;
- rdfs:range :Generation ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "generatedAsDerivation" ;
- :sharesDefinitionWith :Generation .
-
-:hadMember
- a owl:ObjectProperty ;
- rdfs:domain :Collection ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadMember" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- :category "expanded" ;
- :component "expanded" ;
- :inverse "wasMemberOf" ;
- :sharesDefinitionWith :Collection .
-
-:hadPlan
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Plan adopted by an Agent in Association with some Activity. Plan specifications are out of the scope of this specification."@en ;
- rdfs:domain :Association ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadPlan" ;
- rdfs:range :Plan ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "wasPlanOf" ;
- :sharesDefinitionWith :Plan .
-
-:hadPrimarySource
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadPrimarySource" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasDerivedFrom ;
- owl:propertyChainAxiom (:qualifiedPrimarySource
- :entity
- ) ;
- :category "expanded" ;
- :component "derivations" ;
- :inverse "wasPrimarySourceOf" ;
- :qualifiedForm :PrimarySource, :qualifiedPrimarySource .
-
-:hadRole
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Role that an Entity assumed in the context of an Activity. For example, :baking prov:used :spoon; prov:qualified [ a prov:Usage; prov:entity :spoon; prov:hadRole roles:mixing_implement ]."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain :Influence, [
- a owl:Class ;
- owl:unionOf (:Association
- :InstantaneousEvent
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadRole" ;
- rdfs:range :Role ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :editorsDefinition "prov:hadRole references the Role (i.e. the function of an entity with respect to an activity), in the context of an instantaneous usage, generation, association, start, and end."@en ;
- :inverse "wasRoleIn" ;
- :sharesDefinitionWith :Role .
-
-:hadUsage
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Usage involved in an Entity's Derivation."@en ;
- rdfs:domain :Derivation ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadUsage" ;
- rdfs:range :Usage ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "wasUsedInDerivation" ;
- :sharesDefinitionWith :Usage .
-
-:influenced
- a owl:ObjectProperty ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "influenced" ;
- owl:inverseOf :wasInfluencedBy ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :inverse "wasInfluencedBy" ;
- :sharesDefinitionWith :Influence .
-
-:influencer
- a owl:ObjectProperty ;
- rdfs:comment "Subproperties of prov:influencer are used to cite the object of an unqualified PROV-O triple whose predicate is a subproperty of prov:wasInfluencedBy (e.g. prov:used, prov:wasGeneratedBy). prov:influencer is used much like rdf:object is used."@en ;
- rdfs:domain :Influence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "influencer" ;
- rdfs:range owl:Thing ;
- :category "qualified" ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence"^^xsd:anyURI ;
- :editorialNote "This property and its subproperties are used in the same way as the rdf:object property, i.e. to reference the object of an unqualified prov:wasInfluencedBy or prov:influenced triple."@en ;
- :editorsDefinition "This property is used as part of the qualified influence pattern. Subclasses of prov:Influence use these subproperties to reference the resource (Entity, Agent, or Activity) whose influence is being qualified."@en ;
- :inverse "hadInfluence" .
-
-:invalidated
- a owl:ObjectProperty ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "invalidated" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :influenced ;
- owl:inverseOf :wasInvalidatedBy ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "prov:invalidated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions."@en ;
- :inverse "wasInvalidatedBy" ;
- :sharesDefinitionWith :Invalidation .
-
-:invalidatedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an entity was invalidated (i.e., no longer usable)."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "invalidatedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedInvalidation o prov:atTime) rdfs:subPropertyOf prov:invalidatedAtTime."@en ;
- :qualifiedForm :Invalidation, :atTime .
-
-:inverse
- a owl:AnnotationProperty ;
- rdfs:comment "PROV-O does not define all property inverses. The directionalities defined in PROV-O should be given preference over those not defined. However, if users wish to name the inverse of a PROV-O property, the local name given by prov:inverse should be used."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:seeAlso <http://www.w3.org/TR/prov-o/#names-of-inverse-properties> .
-
-:n
- a owl:AnnotationProperty ;
- rdfs:comment "A reference to the principal section of the PROV-DM document that describes this concept."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:order
- a owl:AnnotationProperty ;
- rdfs:comment "The position that this OWL term should be listed within documentation. The scope of the documentation (e.g., among all terms, among terms within a prov:category, among properties applying to a particular class, etc.) is unspecified."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:qualifiedAssociation
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasAssociatedWith Agent :ag, then it can qualify the Association using prov:qualifiedAssociation [ a prov:Association; prov:agent :ag; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedAssociation" ;
- rdfs:range :Association ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "qualifiedAssociationOf" ;
- :sharesDefinitionWith :Association ;
- :unqualifiedForm :wasAssociatedWith .
-
-:qualifiedAttribution
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasAttributedTo Agent :ag, then it can qualify how it was influenced using prov:qualifiedAttribution [ a prov:Attribution; prov:agent :ag; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedAttribution" ;
- rdfs:range :Attribution ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "qualifiedAttributionOf" ;
- :sharesDefinitionWith :Attribution ;
- :unqualifiedForm :wasAttributedTo .
-
-:qualifiedCommunication
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasInformedBy Activity :a, then it can qualify how it was influenced using prov:qualifiedCommunication [ a prov:Communication; prov:activity :a; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedCommunication" ;
- rdfs:range :Communication ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedCommunicationOf" ;
- :qualifiedForm :Communication ;
- :sharesDefinitionWith :Communication .
-
-:qualifiedDelegation
- a owl:ObjectProperty ;
- rdfs:comment "If this Agent prov:actedOnBehalfOf Agent :ag, then it can qualify how with prov:qualifiedResponsibility [ a prov:Responsibility; prov:agent :ag; :foo :bar ]."@en ;
- rdfs:domain :Agent ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedDelegation" ;
- rdfs:range :Delegation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "qualifiedDelegationOf" ;
- :sharesDefinitionWith :Delegation ;
- :unqualifiedForm :actedOnBehalfOf .
-
-:qualifiedDerivation
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasDerivedFrom Entity :e, then it can qualify how it was derived using prov:qualifiedDerivation [ a prov:Derivation; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedDerivation" ;
- rdfs:range :Derivation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedDerivationOf" ;
- :sharesDefinitionWith :Derivation ;
- :unqualifiedForm :wasDerivedFrom .
-
-:qualifiedEnd
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasEndedBy Entity :e1, then it can qualify how it was ended using prov:qualifiedEnd [ a prov:End; prov:entity :e1; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedEnd" ;
- rdfs:range :End ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedEndOf" ;
- :sharesDefinitionWith :End ;
- :unqualifiedForm :wasEndedBy .
-
-:qualifiedForm
- a owl:AnnotationProperty ;
- rdfs:comment """This annotation property links a subproperty of prov:wasInfluencedBy with the subclass of prov:Influence and the qualifying property that are used to qualify it.
-
-Example annotation:
-
- prov:wasGeneratedBy prov:qualifiedForm prov:qualifiedGeneration, prov:Generation .
-
-Then this unqualified assertion:
-
- :entity1 prov:wasGeneratedBy :activity1 .
-
-can be qualified by adding:
-
- :entity1 prov:qualifiedGeneration :entity1Gen .
- :entity1Gen
- a prov:Generation, prov:Influence;
- prov:activity :activity1;
- :customValue 1337 .
-
-Note how the value of the unqualified influence (prov:wasGeneratedBy :activity1) is mirrored as the value of the prov:activity (or prov:entity, or prov:agent) property on the influence class."""@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:qualifiedGeneration
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:generated Entity :e, then it can qualify how it performed the Generation using prov:qualifiedGeneration [ a prov:Generation; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedGeneration" ;
- rdfs:range :Generation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedGenerationOf" ;
- :sharesDefinitionWith :Generation ;
- :unqualifiedForm :wasGeneratedBy .
-
-:qualifiedInfluence
- a owl:ObjectProperty ;
- rdfs:comment "Because prov:qualifiedInfluence is a broad relation, the more specific relations (qualifiedCommunication, qualifiedDelegation, qualifiedEnd, etc.) should be used when applicable."@en ;
- rdfs:domain [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedInfluence" ;
- rdfs:range :Influence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedInfluenceOf" ;
- :sharesDefinitionWith :Influence ;
- :unqualifiedForm :wasInfluencedBy .
-
-:qualifiedInvalidation
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasInvalidatedBy Activity :a, then it can qualify how it was invalidated using prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :a; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedInvalidation" ;
- rdfs:range :Invalidation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedInvalidationOf" ;
- :sharesDefinitionWith :Invalidation ;
- :unqualifiedForm :wasInvalidatedBy .
-
-:qualifiedPrimarySource
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:hadPrimarySource Entity :e, then it can qualify how using prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedPrimarySource" ;
- rdfs:range :PrimarySource ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedSourceOf" ;
- :sharesDefinitionWith :PrimarySource ;
- :unqualifiedForm :hadPrimarySource .
-
-:qualifiedQuotation
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasQuotedFrom Entity :e, then it can qualify how using prov:qualifiedQuotation [ a prov:Quotation; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedQuotation" ;
- rdfs:range :Quotation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedQuotationOf" ;
- :sharesDefinitionWith :Quotation ;
- :unqualifiedForm :wasQuotedFrom .
-
-:qualifiedRevision
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasRevisionOf Entity :e, then it can qualify how it was revised using prov:qualifiedRevision [ a prov:Revision; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedRevision" ;
- rdfs:range :Revision ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "revisedEntity" ;
- :sharesDefinitionWith :Revision ;
- :unqualifiedForm :wasRevisionOf .
-
-:qualifiedStart
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasStartedBy Entity :e1, then it can qualify how it was started using prov:qualifiedStart [ a prov:Start; prov:entity :e1; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedStart" ;
- rdfs:range :Start ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedStartOf" ;
- :sharesDefinitionWith :Start ;
- :unqualifiedForm :wasStartedBy .
-
-:qualifiedUsage
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:used Entity :e, then it can qualify how it used it using prov:qualifiedUsage [ a prov:Usage; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedUsage" ;
- rdfs:range :Usage ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedUsingActivity" ;
- :sharesDefinitionWith :Usage ;
- :unqualifiedForm :used .
-
-:sharesDefinitionWith
- a owl:AnnotationProperty ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:specializationOf
- a owl:AnnotationProperty, owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "specializationOf" ;
- rdfs:range :Entity ;
- rdfs:seeAlso :alternateOf ;
- rdfs:subPropertyOf :alternateOf ;
- :category "expanded" ;
- :component "alternate" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "An entity that is a specialization of another shares all aspects of the latter, and additionally presents more specific aspects of the same thing as the latter. In particular, the lifetime of the entity being specialized contains that of any specialization. Examples of aspects include a time period, an abstraction, and a context associated with the entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-specialization"^^xsd:anyURI ;
- :inverse "generalizationOf" ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-specialization"^^xsd:anyURI .
-
-:startedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an activity started. See also prov:endedAtTime."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "startedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedStart o prov:atTime) rdfs:subPropertyOf prov:startedAtTime."@en ;
- :qualifiedForm :Start, :atTime .
-
-:todo
- a owl:AnnotationProperty .
-
-:unqualifiedForm
- a owl:AnnotationProperty ;
- rdfs:comment "Classes and properties used to qualify relationships are annotated with prov:unqualifiedForm to indicate the property used to assert an unqualified provenance relation."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:used
- a owl:ObjectProperty ;
- rdfs:comment "A prov:Entity that was used by this prov:Activity. For example, :baking prov:used :spoon, :egg, :oven ."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "used" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedUsage
- :entity
- ) ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :inverse "wasUsedBy" ;
- :qualifiedForm :Usage, :qualifiedUsage .
-
-:value
- a owl:DatatypeProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "value" ;
- :category "expanded" ;
- :component "entities-activities" ;
- :definition "Provides a value that is a direct representation of an entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-value"^^xsd:anyURI ;
- :editorialNote "The editor's definition comes from http://www.w3.org/TR/rdf-primer/#rdfvalue", "This property serves the same purpose as rdf:value, but has been reintroduced to avoid some of the definitional ambiguity in the RDF specification (specifically, 'may be used in describing structured values')."@en .
-
-:wasAssociatedWith
- a owl:ObjectProperty ;
- rdfs:comment "An prov:Agent that had some (unspecified) responsibility for the occurrence of this prov:Activity."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasAssociatedWith" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedAssociation
- :agent
- ) ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :inverse "wasAssociateFor" ;
- :qualifiedForm :Association, :qualifiedAssociation .
-
-:wasAttributedTo
- a owl:ObjectProperty ;
- rdfs:comment "Attribution is the ascribing of an entity to an agent."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasAttributedTo" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedAttribution
- :agent
- ) ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :definition "Attribution is the ascribing of an entity to an agent."@en ;
- :inverse "contributed" ;
- :qualifiedForm :Attribution, :qualifiedAttribution .
-
-:wasDerivedFrom
- a owl:ObjectProperty ;
- rdfs:comment "The more specific subproperties of prov:wasDerivedFrom (i.e., prov:wasQuotedFrom, prov:wasRevisionOf, prov:hadPrimarySource) should be used when applicable."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasDerivedFrom" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedDerivation
- :entity
- ) ;
- :category "starting-point" ;
- :component "derivations" ;
- :definition "A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity."@en ;
- :inverse "hadDerivation" ;
- :qualifiedForm :Derivation, :qualifiedDerivation .
-
-:wasEndedBy
- a owl:ObjectProperty ;
- rdfs:comment "End is when an activity is deemed to have ended. An end may refer to an entity, known as trigger, that terminated the activity."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasEndedBy" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedEnd
- :entity
- ) ;
- :category "expanded" ;
- :component "entities-activities" ;
- :inverse "ended" ;
- :qualifiedForm :End, :qualifiedEnd .
-
-:wasGeneratedBy
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasGeneratedBy" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedGeneration
- :activity
- ) ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :inverse "generated" ;
- :qualifiedForm :Generation, :qualifiedGeneration .
-
-:wasInfluencedBy
- a owl:ObjectProperty ;
- rdfs:comment "Because prov:wasInfluencedBy is a broad relation, its more specific subproperties (e.g. prov:wasInformedBy, prov:actedOnBehalfOf, prov:wasEndedBy, etc.) should be used when applicable."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasInfluencedBy" ;
- rdfs:range [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :editorialNote """The sub-properties of prov:wasInfluencedBy can be elaborated in more detail using the Qualification Pattern. For example, the binary relation :baking prov:used :spoon can be qualified by asserting :baking prov:qualifiedUsage [ a prov:Usage; prov:entity :spoon; prov:atLocation :kitchen ] .
-
-Subproperties of prov:wasInfluencedBy may also be asserted directly without being qualified.
-
-prov:wasInfluencedBy should not be used without also using one of its subproperties.
-"""@en ;
- :inverse "influenced" ;
- :qualifiedForm :Influence, :qualifiedInfluence ;
- :sharesDefinitionWith :Influence .
-
-:wasInformedBy
- a owl:ObjectProperty ;
- rdfs:comment "An activity a2 is dependent on or informed by another activity a1, by way of some unspecified entity that is generated by a1 and used by a2."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasInformedBy" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedCommunication
- :activity
- ) ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :inverse "informed" ;
- :qualifiedForm :Communication, :qualifiedCommunication .
-
-:wasInvalidatedBy
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasInvalidatedBy" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedInvalidation
- :activity
- ) ;
- :category "expanded" ;
- :component "entities-activities" ;
- :inverse "invalidated" ;
- :qualifiedForm :Invalidation, :qualifiedInvalidation .
-
-:wasQuotedFrom
- a owl:ObjectProperty ;
- rdfs:comment "An entity is derived from an original entity by copying, or 'quoting', some or all of it."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasQuotedFrom" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasDerivedFrom ;
- owl:propertyChainAxiom (:qualifiedQuotation
- :entity
- ) ;
- :category "expanded" ;
- :component "derivations" ;
- :inverse "quotedAs" ;
- :qualifiedForm :Quotation, :qualifiedQuotation .
-
-:wasRevisionOf
- a owl:AnnotationProperty, owl:ObjectProperty ;
- rdfs:comment "A revision is a derivation that revises an entity into a revised version."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasRevisionOf" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasDerivedFrom ;
- owl:propertyChainAxiom (:qualifiedRevision
- :entity
- ) ;
- :category "expanded" ;
- :component "derivations" ;
- :inverse "hadRevision" ;
- :qualifiedForm :Revision, :qualifiedRevision .
-
-:wasStartedBy
- a owl:ObjectProperty ;
- rdfs:comment "Start is when an activity is deemed to have started. A start may refer to an entity, known as trigger, that initiated the activity."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasStartedBy" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedStart
- :entity
- ) ;
- :category "expanded" ;
- :component "entities-activities" ;
- :inverse "started" ;
- :qualifiedForm :Start, :qualifiedStart .
-
-<http://www.w3.org/ns/prov-o#>
- a owl:Ontology ;
- rdfs:comment """This document is published by the Provenance Working Group (http://www.w3.org/2011/prov/wiki/Main_Page).
-
-If you wish to make comments regarding this document, please send them to public-prov-comments@w3.org (subscribe public-prov-comments-request@w3.org, archives http://lists.w3.org/Archives/Public/public-prov-comments/). All feedback is welcome."""@en ;
- rdfs:label "W3C PROVenance Interchange Ontology (PROV-O)"@en ;
- rdfs:seeAlso <http://www.w3.org/TR/prov-o/>, <http://www.w3.org/ns/prov> ;
- owl:versionIRI <http://www.w3.org/ns/prov-o-20130312> ;
- owl:versionInfo "Proposed Recommendation version 2013-03-12"@en ;
- :specializationOf <http://www.w3.org/ns/prov-o> ;
- :wasRevisionOf <http://www.w3.org/ns/prov-o-20121211> .
-
-[]
- a owl:Axiom ;
- rdfs:comment "A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections."@en ;
- owl:annotatedProperty rdfs:range ;
- owl:annotatedSource :hadMember ;
- owl:annotatedTarget :Entity ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection" .
-
-[]
- a owl:Axiom ;
- rdfs:comment "hadPrimarySource property is a particular case of wasDerivedFrom (see http://www.w3.org/TR/prov-dm/#term-original-source) that aims to give credit to the source that originated some information." ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :hadPrimarySource ;
- owl:annotatedTarget :wasDerivedFrom .
-
-[]
- a owl:Axiom ;
- rdfs:comment "Attribution is a particular case of trace (see http://www.w3.org/TR/prov-dm/#concept-trace), in the sense that it links an entity to the agent that ascribed it." ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasAttributedTo ;
- owl:annotatedTarget :wasInfluencedBy ;
- :definition "IF wasAttributedTo(e2,ag1,aAttr) holds, THEN wasInfluencedBy(e2,ag1) also holds. " .
-
-[]
- a owl:Axiom ;
- rdfs:comment "Derivation is a particular case of trace (see http://www.w3.org/TR/prov-dm/#term-trace), since it links an entity to another entity that contributed to its existence." ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasDerivedFrom ;
- owl:annotatedTarget :wasInfluencedBy .
-
-[]
- a owl:Axiom ;
- owl:annotatedProperty rdfs:range ;
- owl:annotatedSource :wasInfluencedBy ;
- owl:annotatedTarget [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- :definition "influencer: an identifier (o1) for an ancestor entity, activity, or agent that the former depends on;" ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence" .
-
-[]
- a owl:Axiom ;
- owl:annotatedProperty rdfs:domain ;
- owl:annotatedSource :wasInfluencedBy ;
- owl:annotatedTarget [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- :definition "influencee: an identifier (o2) for an entity, activity, or agent; " ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence" .
-
-[]
- a owl:Axiom ;
- rdfs:comment "Quotation is a particular case of derivation (see http://www.w3.org/TR/prov-dm/#term-quotation) in which an entity is derived from an original entity by copying, or \"quoting\", some or all of it. " ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasQuotedFrom ;
- owl:annotatedTarget :wasDerivedFrom .
-
-[]
- a owl:Axiom ;
- rdfs:comment """Revision is a derivation (see http://www.w3.org/TR/prov-dm/#term-Revision). Moreover, according to
-http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#term-Revision 23 April 2012 'wasRevisionOf is a strict sub-relation of wasDerivedFrom since two entities e2 and e1 may satisfy wasDerivedFrom(e2,e1) without being a variant of each other.'""" ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasRevisionOf ;
- owl:annotatedTarget :wasDerivedFrom .
-
--- a/ontology/releases/FR-prov-o/ns/prov-o-inverses-20130312.owl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,354 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<rdf:RDF
- xmlns:owl="http://www.w3.org/2002/07/owl#"
- xmlns:prov="http://www.w3.org/ns/prov#"
- xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
- xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
- xmlns:xsd="http://www.w3.org/2001/XMLSchema#" xml:base="http://www.w3.org/ns/prov-o-inverses">
- <rdf:Description rdf:about="prov#actedOnBehalfOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#activity">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#activityOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>activityOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#activity"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#agent">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#agentOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>agentOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#agent"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#alternateOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>alternateOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#alternateOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#atLocation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#contributed">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>contributed</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasAttributedTo"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#ended">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>ended</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasEndedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#entity">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#entityOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>entityOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#entity"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#generalizationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>generalizationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#specializationOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#generated">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>generated</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasGeneratedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#generatedAsDerivation">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>generatedAsDerivation</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadGeneration"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadActivity">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadDelegate">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadDelegate</rdfs:label>
- <owl:inverseOf rdf:resource="prov#actedOnBehalfOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadDerivation">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadDerivation</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasDerivedFrom"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadGeneration">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#influencer"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadMember">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadPlan">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadPrimarySource">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadRevision">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadRevision</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasRevisionOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadRole">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadUsage">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#influenced">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>influenced</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasInfluencedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#influencer">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#informed">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>informed</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasInformedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#invalidated">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>invalidated</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasInvalidatedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#locationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>locationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#atLocation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAssociation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAssociationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedAssociationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedAssociation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAttribution">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAttributionOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedAttributionOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedAttribution"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedCommunication">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedCommunicationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedCommunicationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedCommunication"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDelegation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDelegationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedDelegationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedDelegation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDerivation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDerivationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedDerivationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedDerivation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedEnd">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedEndOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedEndOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedEnd"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedGeneration">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedGenerationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedGenerationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedGeneration"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInfluence">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInfluenceOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedInfluenceOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedInfluence"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInvalidation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInvalidationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedInvalidationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedInvalidation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedPrimarySource">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedQuotation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedQuotationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedQuotationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedQuotation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedRevision">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedSourceOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedSourceOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedPrimarySource"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedStart">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedStartOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedStartOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedStart"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedUsage">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedUsingActivity">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedUsingActivity</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedUsage"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#quotedAs">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>quotedAs</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasQuotedFrom"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#revisedEntity">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>revisedEntity</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedRevision"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#specializationOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#started">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>started</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasStartedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#used">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasActivityOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasActivityOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadActivity"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasAssociateFor">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasAssociateFor</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasAssociatedWith"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasAssociatedWith">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasAttributedTo">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasDerivedFrom">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasEndedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasGeneratedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasGeneratedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#generated"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasInfluencedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasInfluencedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#influenced"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasInformedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasInvalidatedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasInvalidatedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#invalidated"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasMemberOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasMemberOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadMember"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasPlanOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasPlanOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadPlan"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasPrimarySourceOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasPrimarySourceOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadPrimarySource"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasQuotedFrom">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasRevisionOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasRoleIn">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasRoleIn</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadRole"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasStartedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasUsedBy">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasUsedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#used"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasUsedInDerivation">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasUsedInDerivation</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadUsage"/>
- </rdf:Description>
- <owl:Ontology rdf:about="#">
- <rdfs:seeAlso rdf:resource="../TR/prov-o/#names-of-inverse-properties"/>
- <owl:imports rdf:resource="prov-o#"/>
- <owl:versionIRI rdf:resource="prov-o-inverses-20130312"/>
- <prov:specializationOf rdf:resource=""/>
- <prov:wasDerivedFrom rdf:resource="prov-o-20130312"/>
- <prov:wasRevisionOf rdf:resource="prov-o-inverses-20121211"/>
- </owl:Ontology>
-</rdf:RDF>
--- a/ontology/releases/FR-prov-o/ns/prov-o-inverses-20130312.ttl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,366 +0,0 @@
-@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-
-<#> a owl:Ontology;
- owl:versionIRI <http://www.w3.org/ns/prov-o-inverses-20130312>;
- prov:wasRevisionOf <http://www.w3.org/ns/prov-o-inverses-20121211>;
- prov:specializationOf <http://www.w3.org/ns/prov-o-inverses>;
- prov:wasDerivedFrom <http://www.w3.org/ns/prov-o-20130312>;
- owl:imports <http://www.w3.org/ns/prov-o#>;
- rdfs:seeAlso <http://www.w3.org/TR/prov-o/#names-of-inverse-properties> .
-
-prov:hadDelegate
- rdfs:label "hadDelegate";
- owl:inverseOf prov:actedOnBehalfOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:actedOnBehalfOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:activityOfInfluence
- rdfs:label "activityOfInfluence";
- owl:inverseOf prov:activity;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:activity rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:agentOfInfluence
- rdfs:label "agentOfInfluence";
- owl:inverseOf prov:agent;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:agent rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:alternateOf
- rdfs:label "alternateOf";
- owl:inverseOf prov:alternateOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:alternateOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:locationOf
- rdfs:label "locationOf";
- owl:inverseOf prov:atLocation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:atLocation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:entityOfInfluence
- rdfs:label "entityOfInfluence";
- owl:inverseOf prov:entity;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:entity rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasGeneratedBy
- rdfs:label "wasGeneratedBy";
- owl:inverseOf prov:generated;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:generated rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasActivityOfInfluence
- rdfs:label "wasActivityOfInfluence";
- owl:inverseOf prov:hadActivity;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadActivity rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:generatedAsDerivation
- rdfs:label "generatedAsDerivation";
- owl:inverseOf prov:hadGeneration;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadGeneration rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasMemberOf
- rdfs:label "wasMemberOf";
- owl:inverseOf prov:hadMember;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadMember rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasPlanOf
- rdfs:label "wasPlanOf";
- owl:inverseOf prov:hadPlan;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadPlan rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasPrimarySourceOf
- rdfs:label "wasPrimarySourceOf";
- owl:inverseOf prov:hadPrimarySource;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadPrimarySource rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasRoleIn
- rdfs:label "wasRoleIn";
- owl:inverseOf prov:hadRole;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadRole rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasUsedInDerivation
- rdfs:label "wasUsedInDerivation";
- owl:inverseOf prov:hadUsage;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadUsage rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasInfluencedBy
- rdfs:label "wasInfluencedBy";
- owl:inverseOf prov:influenced;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:influenced rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:hadInfluence
- rdfs:label "hadInfluence";
- owl:inverseOf prov:influencer;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:influencer rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasInvalidatedBy
- rdfs:label "wasInvalidatedBy";
- owl:inverseOf prov:invalidated;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:invalidated rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedAssociationOf
- rdfs:label "qualifiedAssociationOf";
- owl:inverseOf prov:qualifiedAssociation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedAssociation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedAttributionOf
- rdfs:label "qualifiedAttributionOf";
- owl:inverseOf prov:qualifiedAttribution;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedAttribution rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedCommunicationOf
- rdfs:label "qualifiedCommunicationOf";
- owl:inverseOf prov:qualifiedCommunication;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedCommunication rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedDelegationOf
- rdfs:label "qualifiedDelegationOf";
- owl:inverseOf prov:qualifiedDelegation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedDelegation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedDerivationOf
- rdfs:label "qualifiedDerivationOf";
- owl:inverseOf prov:qualifiedDerivation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedDerivation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedEndOf
- rdfs:label "qualifiedEndOf";
- owl:inverseOf prov:qualifiedEnd;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedEnd rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedGenerationOf
- rdfs:label "qualifiedGenerationOf";
- owl:inverseOf prov:qualifiedGeneration;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedGeneration rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedInfluenceOf
- rdfs:label "qualifiedInfluenceOf";
- owl:inverseOf prov:qualifiedInfluence;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedInfluence rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedInvalidationOf
- rdfs:label "qualifiedInvalidationOf";
- owl:inverseOf prov:qualifiedInvalidation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedInvalidation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedSourceOf
- rdfs:label "qualifiedSourceOf";
- owl:inverseOf prov:qualifiedPrimarySource;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedPrimarySource rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedQuotationOf
- rdfs:label "qualifiedQuotationOf";
- owl:inverseOf prov:qualifiedQuotation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedQuotation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:revisedEntity
- rdfs:label "revisedEntity";
- owl:inverseOf prov:qualifiedRevision;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedRevision rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedStartOf
- rdfs:label "qualifiedStartOf";
- owl:inverseOf prov:qualifiedStart;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedStart rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedUsingActivity
- rdfs:label "qualifiedUsingActivity";
- owl:inverseOf prov:qualifiedUsage;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedUsage rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:generalizationOf
- rdfs:label "generalizationOf";
- owl:inverseOf prov:specializationOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:specializationOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasUsedBy
- rdfs:label "wasUsedBy";
- owl:inverseOf prov:used;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:used rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasAssociateFor
- rdfs:label "wasAssociateFor";
- owl:inverseOf prov:wasAssociatedWith;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasAssociatedWith rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:contributed
- rdfs:label "contributed";
- owl:inverseOf prov:wasAttributedTo;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasAttributedTo rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:hadDerivation
- rdfs:label "hadDerivation";
- owl:inverseOf prov:wasDerivedFrom;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasDerivedFrom rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:ended
- rdfs:label "ended";
- owl:inverseOf prov:wasEndedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasEndedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:generated
- rdfs:label "generated";
- owl:inverseOf prov:wasGeneratedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasGeneratedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:influenced
- rdfs:label "influenced";
- owl:inverseOf prov:wasInfluencedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasInfluencedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:informed
- rdfs:label "informed";
- owl:inverseOf prov:wasInformedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasInformedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:invalidated
- rdfs:label "invalidated";
- owl:inverseOf prov:wasInvalidatedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasInvalidatedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:quotedAs
- rdfs:label "quotedAs";
- owl:inverseOf prov:wasQuotedFrom;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasQuotedFrom rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:hadRevision
- rdfs:label "hadRevision";
- owl:inverseOf prov:wasRevisionOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasRevisionOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:started
- rdfs:label "started";
- owl:inverseOf prov:wasStartedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasStartedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
--- a/ontology/releases/FR-prov-o/ns/prov-o-inverses.owl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,354 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<rdf:RDF
- xmlns:owl="http://www.w3.org/2002/07/owl#"
- xmlns:prov="http://www.w3.org/ns/prov#"
- xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
- xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
- xmlns:xsd="http://www.w3.org/2001/XMLSchema#" xml:base="http://www.w3.org/ns/prov-o-inverses">
- <rdf:Description rdf:about="prov#actedOnBehalfOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#activity">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#activityOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>activityOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#activity"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#agent">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#agentOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>agentOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#agent"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#alternateOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>alternateOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#alternateOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#atLocation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#contributed">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>contributed</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasAttributedTo"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#ended">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>ended</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasEndedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#entity">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#entityOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>entityOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#entity"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#generalizationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>generalizationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#specializationOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#generated">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>generated</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasGeneratedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#generatedAsDerivation">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>generatedAsDerivation</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadGeneration"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadActivity">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadDelegate">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadDelegate</rdfs:label>
- <owl:inverseOf rdf:resource="prov#actedOnBehalfOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadDerivation">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadDerivation</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasDerivedFrom"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadGeneration">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#influencer"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadMember">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadPlan">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadPrimarySource">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadRevision">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>hadRevision</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasRevisionOf"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadRole">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#hadUsage">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#influenced">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>influenced</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasInfluencedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#influencer">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#informed">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>informed</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasInformedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#invalidated">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>invalidated</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasInvalidatedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#locationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>locationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#atLocation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAssociation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAssociationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedAssociationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedAssociation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAttribution">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedAttributionOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedAttributionOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedAttribution"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedCommunication">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedCommunicationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedCommunicationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedCommunication"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDelegation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDelegationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedDelegationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedDelegation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDerivation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedDerivationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedDerivationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedDerivation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedEnd">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedEndOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedEndOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedEnd"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedGeneration">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedGenerationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedGenerationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedGeneration"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInfluence">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInfluenceOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedInfluenceOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedInfluence"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInvalidation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedInvalidationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedInvalidationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedInvalidation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedPrimarySource">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedQuotation">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedQuotationOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedQuotationOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedQuotation"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedRevision">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedSourceOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedSourceOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedPrimarySource"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedStart">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedStartOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedStartOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedStart"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedUsage">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#qualifiedUsingActivity">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>qualifiedUsingActivity</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedUsage"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#quotedAs">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>quotedAs</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasQuotedFrom"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#revisedEntity">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>revisedEntity</rdfs:label>
- <owl:inverseOf rdf:resource="prov#qualifiedRevision"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#specializationOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#started">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>started</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasStartedBy"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#used">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasActivityOfInfluence">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasActivityOfInfluence</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadActivity"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasAssociateFor">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasAssociateFor</rdfs:label>
- <owl:inverseOf rdf:resource="prov#wasAssociatedWith"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasAssociatedWith">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasAttributedTo">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasDerivedFrom">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasEndedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasGeneratedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasGeneratedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#generated"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasInfluencedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasInfluencedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#influenced"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasInformedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasInvalidatedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasInvalidatedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#invalidated"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasMemberOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasMemberOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadMember"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasPlanOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasPlanOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadPlan"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasPrimarySourceOf">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasPrimarySourceOf</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadPrimarySource"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasQuotedFrom">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasRevisionOf">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasRoleIn">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasRoleIn</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadRole"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasStartedBy">
- <rdfs:isDefinedBy rdf:resource="prov-o#"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasUsedBy">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasUsedBy</rdfs:label>
- <owl:inverseOf rdf:resource="prov#used"/>
- </rdf:Description>
- <rdf:Description rdf:about="prov#wasUsedInDerivation">
- <rdfs:isDefinedBy rdf:resource="#"/>
- <rdfs:label>wasUsedInDerivation</rdfs:label>
- <owl:inverseOf rdf:resource="prov#hadUsage"/>
- </rdf:Description>
- <owl:Ontology rdf:about="#">
- <rdfs:seeAlso rdf:resource="../TR/prov-o/#names-of-inverse-properties"/>
- <owl:imports rdf:resource="prov-o#"/>
- <owl:versionIRI rdf:resource="prov-o-inverses-20130312"/>
- <prov:specializationOf rdf:resource=""/>
- <prov:wasDerivedFrom rdf:resource="prov-o-20130312"/>
- <prov:wasRevisionOf rdf:resource="prov-o-inverses-20121211"/>
- </owl:Ontology>
-</rdf:RDF>
--- a/ontology/releases/FR-prov-o/ns/prov-o-inverses.ttl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,366 +0,0 @@
-@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix prov: <http://www.w3.org/ns/prov#> .
-
-<#> a owl:Ontology;
- owl:versionIRI <http://www.w3.org/ns/prov-o-inverses-20130312>;
- prov:wasRevisionOf <http://www.w3.org/ns/prov-o-inverses-20121211>;
- prov:specializationOf <http://www.w3.org/ns/prov-o-inverses>;
- prov:wasDerivedFrom <http://www.w3.org/ns/prov-o-20130312>;
- owl:imports <http://www.w3.org/ns/prov-o#>;
- rdfs:seeAlso <http://www.w3.org/TR/prov-o/#names-of-inverse-properties> .
-
-prov:hadDelegate
- rdfs:label "hadDelegate";
- owl:inverseOf prov:actedOnBehalfOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:actedOnBehalfOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:activityOfInfluence
- rdfs:label "activityOfInfluence";
- owl:inverseOf prov:activity;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:activity rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:agentOfInfluence
- rdfs:label "agentOfInfluence";
- owl:inverseOf prov:agent;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:agent rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:alternateOf
- rdfs:label "alternateOf";
- owl:inverseOf prov:alternateOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:alternateOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:locationOf
- rdfs:label "locationOf";
- owl:inverseOf prov:atLocation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:atLocation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:entityOfInfluence
- rdfs:label "entityOfInfluence";
- owl:inverseOf prov:entity;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:entity rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasGeneratedBy
- rdfs:label "wasGeneratedBy";
- owl:inverseOf prov:generated;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:generated rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasActivityOfInfluence
- rdfs:label "wasActivityOfInfluence";
- owl:inverseOf prov:hadActivity;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadActivity rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:generatedAsDerivation
- rdfs:label "generatedAsDerivation";
- owl:inverseOf prov:hadGeneration;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadGeneration rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasMemberOf
- rdfs:label "wasMemberOf";
- owl:inverseOf prov:hadMember;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadMember rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasPlanOf
- rdfs:label "wasPlanOf";
- owl:inverseOf prov:hadPlan;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadPlan rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasPrimarySourceOf
- rdfs:label "wasPrimarySourceOf";
- owl:inverseOf prov:hadPrimarySource;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadPrimarySource rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasRoleIn
- rdfs:label "wasRoleIn";
- owl:inverseOf prov:hadRole;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadRole rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasUsedInDerivation
- rdfs:label "wasUsedInDerivation";
- owl:inverseOf prov:hadUsage;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:hadUsage rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasInfluencedBy
- rdfs:label "wasInfluencedBy";
- owl:inverseOf prov:influenced;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:influenced rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:hadInfluence
- rdfs:label "hadInfluence";
- owl:inverseOf prov:influencer;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:influencer rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasInvalidatedBy
- rdfs:label "wasInvalidatedBy";
- owl:inverseOf prov:invalidated;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:invalidated rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedAssociationOf
- rdfs:label "qualifiedAssociationOf";
- owl:inverseOf prov:qualifiedAssociation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedAssociation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedAttributionOf
- rdfs:label "qualifiedAttributionOf";
- owl:inverseOf prov:qualifiedAttribution;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedAttribution rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedCommunicationOf
- rdfs:label "qualifiedCommunicationOf";
- owl:inverseOf prov:qualifiedCommunication;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedCommunication rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedDelegationOf
- rdfs:label "qualifiedDelegationOf";
- owl:inverseOf prov:qualifiedDelegation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedDelegation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedDerivationOf
- rdfs:label "qualifiedDerivationOf";
- owl:inverseOf prov:qualifiedDerivation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedDerivation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedEndOf
- rdfs:label "qualifiedEndOf";
- owl:inverseOf prov:qualifiedEnd;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedEnd rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedGenerationOf
- rdfs:label "qualifiedGenerationOf";
- owl:inverseOf prov:qualifiedGeneration;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedGeneration rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedInfluenceOf
- rdfs:label "qualifiedInfluenceOf";
- owl:inverseOf prov:qualifiedInfluence;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedInfluence rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedInvalidationOf
- rdfs:label "qualifiedInvalidationOf";
- owl:inverseOf prov:qualifiedInvalidation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedInvalidation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedSourceOf
- rdfs:label "qualifiedSourceOf";
- owl:inverseOf prov:qualifiedPrimarySource;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedPrimarySource rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedQuotationOf
- rdfs:label "qualifiedQuotationOf";
- owl:inverseOf prov:qualifiedQuotation;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedQuotation rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:revisedEntity
- rdfs:label "revisedEntity";
- owl:inverseOf prov:qualifiedRevision;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedRevision rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedStartOf
- rdfs:label "qualifiedStartOf";
- owl:inverseOf prov:qualifiedStart;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedStart rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:qualifiedUsingActivity
- rdfs:label "qualifiedUsingActivity";
- owl:inverseOf prov:qualifiedUsage;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:qualifiedUsage rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:generalizationOf
- rdfs:label "generalizationOf";
- owl:inverseOf prov:specializationOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:specializationOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasUsedBy
- rdfs:label "wasUsedBy";
- owl:inverseOf prov:used;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:used rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:wasAssociateFor
- rdfs:label "wasAssociateFor";
- owl:inverseOf prov:wasAssociatedWith;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasAssociatedWith rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:contributed
- rdfs:label "contributed";
- owl:inverseOf prov:wasAttributedTo;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasAttributedTo rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:hadDerivation
- rdfs:label "hadDerivation";
- owl:inverseOf prov:wasDerivedFrom;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasDerivedFrom rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:ended
- rdfs:label "ended";
- owl:inverseOf prov:wasEndedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasEndedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:generated
- rdfs:label "generated";
- owl:inverseOf prov:wasGeneratedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasGeneratedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:influenced
- rdfs:label "influenced";
- owl:inverseOf prov:wasInfluencedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasInfluencedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:informed
- rdfs:label "informed";
- owl:inverseOf prov:wasInformedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasInformedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:invalidated
- rdfs:label "invalidated";
- owl:inverseOf prov:wasInvalidatedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasInvalidatedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:quotedAs
- rdfs:label "quotedAs";
- owl:inverseOf prov:wasQuotedFrom;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasQuotedFrom rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:hadRevision
- rdfs:label "hadRevision";
- owl:inverseOf prov:wasRevisionOf;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasRevisionOf rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
-prov:started
- rdfs:label "started";
- owl:inverseOf prov:wasStartedBy;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov-o-inverses#> .
-
-prov:wasStartedBy rdfs:isDefinedBy <http://www.w3.org/ns/prov-o#> .
-
-
--- a/ontology/releases/FR-prov-o/ns/prov-o.owl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1788 +0,0 @@
-<?xml version="1.0"?>
-
-
-<!DOCTYPE rdf:RDF [
- <!ENTITY owl "http://www.w3.org/2002/07/owl#" >
- <!ENTITY xsd "http://www.w3.org/2001/XMLSchema#" >
- <!ENTITY rdfs "http://www.w3.org/2000/01/rdf-schema#" >
- <!ENTITY rdf "http://www.w3.org/1999/02/22-rdf-syntax-ns#" >
-]>
-
-
-<rdf:RDF xmlns="http://www.w3.org/ns/prov#"
- xml:base="http://www.w3.org/ns/prov"
- xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
- xmlns:owl="http://www.w3.org/2002/07/owl#"
- xmlns:xsd="http://www.w3.org/2001/XMLSchema#"
- xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
- <owl:Ontology rdf:about="http://www.w3.org/ns/prov-o#">
- <rdfs:label xml:lang="en">W3C PROVenance Interchange Ontology (PROV-O)</rdfs:label>
- <owl:versionInfo xml:lang="en">Proposed Recommendation version 2013-03-12</owl:versionInfo>
- <rdfs:comment xml:lang="en">This document is published by the Provenance Working Group (http://www.w3.org/2011/prov/wiki/Main_Page).
-
-If you wish to make comments regarding this document, please send them to public-prov-comments@w3.org (subscribe public-prov-comments-request@w3.org, archives http://lists.w3.org/Archives/Public/public-prov-comments/). All feedback is welcome.</rdfs:comment>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/TR/prov-o/"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov"/>
- <specializationOf rdf:resource="http://www.w3.org/ns/prov-o"/>
- <wasRevisionOf rdf:resource="http://www.w3.org/ns/prov-o-20121211"/>
- <owl:versionIRI rdf:resource="http://www.w3.org/ns/prov-o-20130312"/>
- </owl:Ontology>
-
- <owl:Ontology rdf:about="http://www.w3.org/ns/prov#"></owl:Ontology>
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Annotation properties
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#unqualifiedForm">
- <rdfs:comment xml:lang="en">Classes and properties used to qualify relationships are annotated with prov:unqualifiedForm to indicate the property used to assert an unqualified provenance relation.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#wasRevisionOf">
- <rdfs:label>wasRevisionOf</rdfs:label>
- <component>derivations</component>
- <rdfs:comment xml:lang="en">A revision is a derivation that revises an entity into a revised version.</rdfs:comment>
- <inverse>hadRevision</inverse>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedRevision"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#aq">
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#sharesDefinitionWith">
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#definition">
- <rdfs:comment xml:lang="en">A definition quoted from PROV-DM or PROV-CONSTRAINTS that describes the concept expressed with this OWL term.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#editorialNote">
- <rdfs:comment xml:lang="en">A note by the OWL development team about how this term expresses the PROV-DM concept, or how it should be used in context of semantic web or linked data.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&rdfs;label">
- <rdfs:comment xml:lang="en"></rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#inverse">
- <rdfs:comment xml:lang="en">PROV-O does not define all property inverses. The directionalities defined in PROV-O should be given preference over those not defined. However, if users wish to name the inverse of a PROV-O property, the local name given by prov:inverse should be used.</rdfs:comment>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/TR/prov-o/#names-of-inverse-properties"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&rdfs;comment">
- <rdfs:comment xml:lang="en"></rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#constraints">
- <rdfs:comment xml:lang="en">A reference to the principal section of the PROV-CONSTRAINTS document that describes this concept.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&owl;versionInfo"/>
- <owl:AnnotationProperty rdf:about="&rdfs;seeAlso">
- <rdfs:comment xml:lang="en"></rdfs:comment>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#specializationOf">
- <rdfs:label>specializationOf</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-specialization</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-specialization</n>
- <component>alternate</component>
- <inverse>generalizationOf</inverse>
- <category>expanded</category>
- <definition xml:lang="en">An entity that is a specialization of another shares all aspects of the latter, and additionally presents more specific aspects of the same thing as the latter. In particular, the lifetime of the entity being specialized contains that of any specialization. Examples of aspects include a time period, an abstraction, and a context associated with the entity.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#alternateOf"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#dm">
- <rdfs:comment xml:lang="en">A reference to the principal section of the PROV-DM document that describes this concept.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#category">
- <rdfs:comment xml:lang="en">Classify prov-o terms into three categories, including 'starting-point', 'qualifed', and 'extended'. This classification is used by the prov-o html document to gently introduce prov-o terms to its users. </rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#order">
- <rdfs:comment xml:lang="en">The position that this OWL term should be listed within documentation. The scope of the documentation (e.g., among all terms, among terms within a prov:category, among properties applying to a particular class, etc.) is unspecified.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="&rdfs;isDefinedBy"/>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#editorsDefinition">
- <rdfs:comment xml:lang="en">When the prov-o term does not have a definition drawn from prov-dm, and the prov-o editor provides one.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#definition"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#component">
- <rdfs:comment xml:lang="en">Classify prov-o terms into six components according to prov-dm, including 'agents-responsibility', 'alternate', 'annotations', 'collections', 'derivations', and 'entities-activities'. This classification is used so that readers of prov-o specification can find its correspondence with the prov-dm specification.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#qualifiedForm">
- <rdfs:comment xml:lang="en">This annotation property links a subproperty of prov:wasInfluencedBy with the subclass of prov:Influence and the qualifying property that are used to qualify it.
-
-Example annotation:
-
- prov:wasGeneratedBy prov:qualifiedForm prov:qualifiedGeneration, prov:Generation .
-
-Then this unqualified assertion:
-
- :entity1 prov:wasGeneratedBy :activity1 .
-
-can be qualified by adding:
-
- :entity1 prov:qualifiedGeneration :entity1Gen .
- :entity1Gen
- a prov:Generation, prov:Influence;
- prov:activity :activity1;
- :customValue 1337 .
-
-Note how the value of the unqualified influence (prov:wasGeneratedBy :activity1) is mirrored as the value of the prov:activity (or prov:entity, or prov:agent) property on the influence class.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#todo"/>
- <owl:AnnotationProperty rdf:about="http://www.w3.org/ns/prov#n">
- <rdfs:comment xml:lang="en">A reference to the principal section of the PROV-DM document that describes this concept.</rdfs:comment>
- <rdfs:subPropertyOf rdf:resource="&rdfs;seeAlso"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:AnnotationProperty>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Object Properties
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/ns/prov#actedOnBehalfOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#actedOnBehalfOf">
- <rdfs:label>actedOnBehalfOf</rdfs:label>
- <component>agents-responsibility</component>
- <inverse>hadDelegate</inverse>
- <rdfs:comment xml:lang="en">An object property to express the accountability of an agent towards another agent. The subordinate agent acted on behalf of the responsible agent in an actual activity. </rdfs:comment>
- <category>starting-point</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Delegation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedDelegation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedDelegation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#agent"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#activity -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#activity">
- <rdfs:label>activity</rdfs:label>
- <editorsDefinition>The prov:activity property references an prov:Activity which influenced a resource. This property applies to an prov:ActivityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</editorsDefinition>
- <inverse>activityOfInfluence</inverse>
- <editorialNote xml:lang="en">This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple.</editorialNote>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influencer"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#agent -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#agent">
- <rdfs:label>agent</rdfs:label>
- <editorsDefinition xml:lang="en">The prov:agent property references an prov:Agent which influenced a resource. This property applies to an prov:AgentInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</editorsDefinition>
- <inverse>agentOfInfluence</inverse>
- <editorialNote xml:lang="en">This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple.</editorialNote>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influencer"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#alternateOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#alternateOf">
- <rdfs:label>alternateOf</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-alternate</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-alternate</n>
- <definition xml:lang="en">Two alternate entities present aspects of the same thing. These aspects may be the same or different, and the alternate entities may or may not overlap in time.</definition>
- <category>expanded</category>
- <component>alternate</component>
- <inverse>alternateOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#specializationOf"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#atLocation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#atLocation">
- <rdfs:label>atLocation</rdfs:label>
- <rdfs:comment xml:lang="en">The Location of any resource.</rdfs:comment>
- <inverse>locationOf</inverse>
- <editorialNote xml:lang="en">The naming of prov:atLocation parallels prov:atTime, and is not named prov:hadLocation to avoid conflicting with the convention that prov:had* properties are used on prov:Influence classes.</editorialNote>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <editorialNote xml:lang="en">This property is not functional because the many values could be at a variety of granularies (In this building, in this room, in that chair).</editorialNote>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Location"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Location"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#entity -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#entity">
- <rdfs:label>entity</rdfs:label>
- <editorsDefinition>The prov:entity property references an prov:Entity which influenced a resource. This property applies to an prov:EntityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent.</editorsDefinition>
- <inverse>entityOfInfluence</inverse>
- <editorialNote xml:lang="en">This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple.</editorialNote>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influencer"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#generated -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#generated">
- <rdfs:label>generated</rdfs:label>
- <component>entities-activities</component>
- <inverse>wasGeneratedBy</inverse>
- <category>expanded</category>
- <editorialNote xml:lang="en">prov:generated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions.</editorialNote>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influenced"/>
- <owl:inverseOf rdf:resource="http://www.w3.org/ns/prov#wasGeneratedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadActivity -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadActivity">
- <rdfs:label>hadActivity</rdfs:label>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <rdfs:comment xml:lang="en">The _optional_ Activity of an Influence, which used, generated, invalidated, or was the responsibility of some Entity. This property is _not_ used by ActivityInfluence (use prov:activity instead).</rdfs:comment>
- <editorialNote xml:lang="en">The multiple rdfs:domain assertions are intended. One is simpler and works for OWL-RL, the union is more specific but is not recognized by OWL-RL.</editorialNote>
- <component>derivations</component>
- <category>qualified</category>
- <inverse>wasActivityOfInfluence</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Delegation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Derivation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#End"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Start"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadGeneration -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadGeneration">
- <rdfs:label>hadGeneration</rdfs:label>
- <inverse>generatedAsDerivation</inverse>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The _optional_ Generation involved in an Entity's Derivation.</rdfs:comment>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadMember -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadMember">
- <rdfs:label>hadMember</rdfs:label>
- <category>expanded</category>
- <component>expanded</component>
- <inverse>wasMemberOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Collection"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Collection"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment xml:lang="en">A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections.</rdfs:comment>
- <dm>http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection</dm>
- <owl:annotatedProperty rdf:resource="&rdfs;range"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#hadMember"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadPlan -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadPlan">
- <rdfs:label>hadPlan</rdfs:label>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <inverse>wasPlanOf</inverse>
- <rdfs:comment xml:lang="en">The _optional_ Plan adopted by an Agent in Association with some Activity. Plan specifications are out of the scope of this specification.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Plan"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Plan"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadPrimarySource -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadPrimarySource">
- <rdfs:label>hadPrimarySource</rdfs:label>
- <component>derivations</component>
- <category>expanded</category>
- <inverse>wasPrimarySourceOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#PrimarySource"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedPrimarySource"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedPrimarySource"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>hadPrimarySource property is a particular case of wasDerivedFrom (see http://www.w3.org/TR/prov-dm/#term-original-source) that aims to give credit to the source that originated some information.</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#hadPrimarySource"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadRole -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadRole">
- <rdfs:label>hadRole</rdfs:label>
- <component>agents-responsibility</component>
- <inverse>wasRoleIn</inverse>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The _optional_ Role that an Entity assumed in the context of an Activity. For example, :baking prov:used :spoon; prov:qualified [ a prov:Usage; prov:entity :spoon; prov:hadRole roles:mixing_implement ].</rdfs:comment>
- <editorsDefinition xml:lang="en">prov:hadRole references the Role (i.e. the function of an entity with respect to an activity), in the context of an instantaneous usage, generation, association, start, and end.</editorsDefinition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Role"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Role"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Association"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#hadUsage -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#hadUsage">
- <rdfs:label>hadUsage</rdfs:label>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The _optional_ Usage involved in an Entity's Derivation.</rdfs:comment>
- <inverse>wasUsedInDerivation</inverse>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#influenced -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#influenced">
- <rdfs:label>influenced</rdfs:label>
- <inverse>wasInfluencedBy</inverse>
- <component>agents-responsibility</component>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <owl:inverseOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#influencer -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#influencer">
- <rdfs:label>influencer</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <category>qualified</category>
- <inverse>hadInfluence</inverse>
- <rdfs:comment xml:lang="en">Subproperties of prov:influencer are used to cite the object of an unqualified PROV-O triple whose predicate is a subproperty of prov:wasInfluencedBy (e.g. prov:used, prov:wasGeneratedBy). prov:influencer is used much like rdf:object is used.</rdfs:comment>
- <editorialNote xml:lang="en">This property and its subproperties are used in the same way as the rdf:object property, i.e. to reference the object of an unqualified prov:wasInfluencedBy or prov:influenced triple.</editorialNote>
- <editorsDefinition xml:lang="en">This property is used as part of the qualified influence pattern. Subclasses of prov:Influence use these subproperties to reference the resource (Entity, Agent, or Activity) whose influence is being qualified.</editorsDefinition>
- <rdfs:range rdf:resource="&owl;Thing"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#invalidated -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#invalidated">
- <rdfs:label>invalidated</rdfs:label>
- <category>expanded</category>
- <inverse>wasInvalidatedBy</inverse>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">prov:invalidated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions.</editorialNote>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#influenced"/>
- <owl:inverseOf rdf:resource="http://www.w3.org/ns/prov#wasInvalidatedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedAssociation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedAssociation">
- <rdfs:label>qualifiedAssociation</rdfs:label>
- <inverse>qualifiedAssociationOf</inverse>
- <rdfs:comment xml:lang="en">If this Activity prov:wasAssociatedWith Agent :ag, then it can qualify the Association using prov:qualifiedAssociation [ a prov:Association; prov:agent :ag; :foo :bar ].</rdfs:comment>
- <component>agents-responsibility</component>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAssociatedWith"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedAttribution -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedAttribution">
- <rdfs:label>qualifiedAttribution</rdfs:label>
- <inverse>qualifiedAttributionOf</inverse>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:comment xml:lang="en">If this Entity prov:wasAttributedTo Agent :ag, then it can qualify how it was influenced using prov:qualifiedAttribution [ a prov:Attribution; prov:agent :ag; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Attribution"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Attribution"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAttributedTo"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedCommunication -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedCommunication">
- <rdfs:label>qualifiedCommunication</rdfs:label>
- <inverse>qualifiedCommunicationOf</inverse>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:wasInformedBy Activity :a, then it can qualify how it was influenced using prov:qualifiedCommunication [ a prov:Communication; prov:activity :a; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedDelegation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedDelegation">
- <rdfs:label>qualifiedDelegation</rdfs:label>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">If this Agent prov:actedOnBehalfOf Agent :ag, then it can qualify how with prov:qualifiedResponsibility [ a prov:Responsibility; prov:agent :ag; :foo :bar ].</rdfs:comment>
- <inverse>qualifiedDelegationOf</inverse>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Delegation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Delegation"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#actedOnBehalfOf"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedDerivation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedDerivation">
- <rdfs:label>qualifiedDerivation</rdfs:label>
- <component>derivations</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">If this Entity prov:wasDerivedFrom Entity :e, then it can qualify how it was derived using prov:qualifiedDerivation [ a prov:Derivation; prov:entity :e; :foo :bar ].</rdfs:comment>
- <inverse>qualifiedDerivationOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedEnd -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedEnd">
- <rdfs:label>qualifiedEnd</rdfs:label>
- <category>qualified</category>
- <inverse>qualifiedEndOf</inverse>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:wasEndedBy Entity :e1, then it can qualify how it was ended using prov:qualifiedEnd [ a prov:End; prov:entity :e1; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#End"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#End"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasEndedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedGeneration -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedGeneration">
- <rdfs:label>qualifiedGeneration</rdfs:label>
- <inverse>qualifiedGenerationOf</inverse>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">If this Activity prov:generated Entity :e, then it can qualify how it performed the Generation using prov:qualifiedGeneration [ a prov:Generation; prov:entity :e; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasGeneratedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedInfluence -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedInfluence">
- <rdfs:label>qualifiedInfluence</rdfs:label>
- <rdfs:comment xml:lang="en">Because prov:qualifiedInfluence is a broad relation, the more specific relations (qualifiedCommunication, qualifiedDelegation, qualifiedEnd, etc.) should be used when applicable.</rdfs:comment>
- <category>qualified</category>
- <inverse>qualifiedInfluenceOf</inverse>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedInvalidation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedInvalidation">
- <rdfs:label>qualifiedInvalidation</rdfs:label>
- <rdfs:comment xml:lang="en">If this Entity prov:wasInvalidatedBy Activity :a, then it can qualify how it was invalidated using prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :a; :foo :bar ].</rdfs:comment>
- <component>entities-activities</component>
- <category>qualified</category>
- <inverse>qualifiedInvalidationOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInvalidatedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedPrimarySource -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedPrimarySource">
- <rdfs:label>qualifiedPrimarySource</rdfs:label>
- <rdfs:comment xml:lang="en">If this Entity prov:hadPrimarySource Entity :e, then it can qualify how using prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :e; :foo :bar ].</rdfs:comment>
- <component>derivations</component>
- <category>qualified</category>
- <inverse>qualifiedSourceOf</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#PrimarySource"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#PrimarySource"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#hadPrimarySource"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedQuotation -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedQuotation">
- <rdfs:label>qualifiedQuotation</rdfs:label>
- <category>qualified</category>
- <inverse>qualifiedQuotationOf</inverse>
- <rdfs:comment xml:lang="en">If this Entity prov:wasQuotedFrom Entity :e, then it can qualify how using prov:qualifiedQuotation [ a prov:Quotation; prov:entity :e; :foo :bar ].</rdfs:comment>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Quotation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Quotation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasQuotedFrom"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedRevision -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedRevision">
- <rdfs:label>qualifiedRevision</rdfs:label>
- <rdfs:comment xml:lang="en">If this Entity prov:wasRevisionOf Entity :e, then it can qualify how it was revised using prov:qualifiedRevision [ a prov:Revision; prov:entity :e; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <inverse>revisedEntity</inverse>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasRevisionOf"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedStart -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedStart">
- <rdfs:label>qualifiedStart</rdfs:label>
- <inverse>qualifiedStartOf</inverse>
- <category>qualified</category>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:wasStartedBy Entity :e1, then it can qualify how it was started using prov:qualifiedStart [ a prov:Start; prov:entity :e1; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasStartedBy"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#qualifiedUsage -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#qualifiedUsage">
- <rdfs:label>qualifiedUsage</rdfs:label>
- <category>qualified</category>
- <inverse>qualifiedUsingActivity</inverse>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">If this Activity prov:used Entity :e, then it can qualify how it used it using prov:qualifiedUsage [ a prov:Usage; prov:entity :e; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#used"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#specializationOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#specializationOf">
- <rdfs:label>specializationOf</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-specialization</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-specialization</n>
- <component>alternate</component>
- <category>expanded</category>
- <inverse>generalizationOf</inverse>
- <definition xml:lang="en">An entity that is a specialization of another shares all aspects of the latter, and additionally presents more specific aspects of the same thing as the latter. In particular, the lifetime of the entity being specialized contains that of any specialization. Examples of aspects include a time period, an abstraction, and a context associated with the entity.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#alternateOf"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#alternateOf"/>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#used -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#used">
- <rdfs:label>used</rdfs:label>
- <inverse>wasUsedBy</inverse>
- <rdfs:comment xml:lang="en">A prov:Entity that was used by this prov:Activity. For example, :baking prov:used :spoon, :egg, :oven .</rdfs:comment>
- <category>starting-point</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Usage"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedUsage"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedUsage"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasAssociatedWith -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasAssociatedWith">
- <rdfs:label>wasAssociatedWith</rdfs:label>
- <component>agents-responsibility</component>
- <inverse>wasAssociateFor</inverse>
- <rdfs:comment xml:lang="en">An prov:Agent that had some (unspecified) responsibility for the occurrence of this prov:Activity.</rdfs:comment>
- <category>starting-point</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Association"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedAssociation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedAssociation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#agent"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasAttributedTo -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasAttributedTo">
- <rdfs:label>wasAttributedTo</rdfs:label>
- <component>agents-responsibility</component>
- <category>starting-point</category>
- <inverse>contributed</inverse>
- <definition xml:lang="en">Attribution is the ascribing of an entity to an agent.</definition>
- <rdfs:comment xml:lang="en">Attribution is the ascribing of an entity to an agent.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Attribution"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedAttribution"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedAttribution"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#agent"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <definition>IF wasAttributedTo(e2,ag1,aAttr) holds, THEN wasInfluencedBy(e2,ag1) also holds. </definition>
- <rdfs:comment>Attribution is a particular case of trace (see http://www.w3.org/TR/prov-dm/#concept-trace), in the sense that it links an entity to the agent that ascribed it.</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasAttributedTo"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasDerivedFrom -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasDerivedFrom">
- <rdfs:label>wasDerivedFrom</rdfs:label>
- <inverse>hadDerivation</inverse>
- <definition xml:lang="en">A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.</definition>
- <category>starting-point</category>
- <rdfs:comment xml:lang="en">The more specific subproperties of prov:wasDerivedFrom (i.e., prov:wasQuotedFrom, prov:wasRevisionOf, prov:hadPrimarySource) should be used when applicable.</rdfs:comment>
- <component>derivations</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedDerivation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedDerivation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>Derivation is a particular case of trace (see http://www.w3.org/TR/prov-dm/#term-trace), since it links an entity to another entity that contributed to its existence.</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasEndedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasEndedBy">
- <rdfs:label>wasEndedBy</rdfs:label>
- <category>expanded</category>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">End is when an activity is deemed to have ended. An end may refer to an entity, known as trigger, that terminated the activity.</rdfs:comment>
- <inverse>ended</inverse>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#End"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedEnd"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedEnd"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasGeneratedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasGeneratedBy">
- <rdfs:label>wasGeneratedBy</rdfs:label>
- <inverse>generated</inverse>
- <category>starting-point</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedGeneration"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedGeneration"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#activity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasInfluencedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasInfluencedBy">
- <rdfs:label>wasInfluencedBy</rdfs:label>
- <rdfs:comment xml:lang="en">Because prov:wasInfluencedBy is a broad relation, its more specific subproperties (e.g. prov:wasInformedBy, prov:actedOnBehalfOf, prov:wasEndedBy, etc.) should be used when applicable.</rdfs:comment>
- <rdfs:comment>This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href="#owl-profile">PROV-O OWL Profile</a>.</rdfs:comment>
- <editorialNote xml:lang="en">The sub-properties of prov:wasInfluencedBy can be elaborated in more detail using the Qualification Pattern. For example, the binary relation :baking prov:used :spoon can be qualified by asserting :baking prov:qualifiedUsage [ a prov:Usage; prov:entity :spoon; prov:atLocation :kitchen ] .
-
-Subproperties of prov:wasInfluencedBy may also be asserted directly without being qualified.
-
-prov:wasInfluencedBy should not be used without also using one of its subproperties.
-</editorialNote>
- <category>qualified</category>
- <inverse>influenced</inverse>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedInfluence"/>
- <rdfs:domain>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:domain>
- <rdfs:range>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </rdfs:range>
- </owl:ObjectProperty>
- <owl:Axiom>
- <definition>influencer: an identifier (o1) for an ancestor entity, activity, or agent that the former depends on;</definition>
- <dm>http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <owl:annotatedProperty rdf:resource="&rdfs;range"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:annotatedTarget>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </owl:annotatedTarget>
- </owl:Axiom>
- <owl:Axiom>
- <dm>http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <definition>influencee: an identifier (o2) for an entity, activity, or agent; </definition>
- <owl:annotatedProperty rdf:resource="&rdfs;domain"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:annotatedTarget>
- <owl:Class>
- <owl:unionOf rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Activity"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Agent"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#Entity"/>
- </owl:unionOf>
- </owl:Class>
- </owl:annotatedTarget>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasInformedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasInformedBy">
- <rdfs:label>wasInformedBy</rdfs:label>
- <inverse>informed</inverse>
- <rdfs:comment xml:lang="en">An activity a2 is dependent on or informed by another activity a1, by way of some unspecified entity that is generated by a1 and used by a2.</rdfs:comment>
- <category>starting-point</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Communication"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedCommunication"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedCommunication"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#activity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasInvalidatedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasInvalidatedBy">
- <rdfs:label>wasInvalidatedBy</rdfs:label>
- <component>entities-activities</component>
- <inverse>invalidated</inverse>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedInvalidation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedInvalidation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#activity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasQuotedFrom -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasQuotedFrom">
- <rdfs:label>wasQuotedFrom</rdfs:label>
- <category>expanded</category>
- <component>derivations</component>
- <inverse>quotedAs</inverse>
- <rdfs:comment xml:lang="en">An entity is derived from an original entity by copying, or 'quoting', some or all of it.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Quotation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedQuotation"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedQuotation"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>Quotation is a particular case of derivation (see http://www.w3.org/TR/prov-dm/#term-quotation) in which an entity is derived from an original entity by copying, or "quoting", some or all of it. </rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasQuotedFrom"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasRevisionOf -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasRevisionOf">
- <rdfs:label>wasRevisionOf</rdfs:label>
- <rdfs:comment xml:lang="en">A revision is a derivation that revises an entity into a revised version.</rdfs:comment>
- <component>derivations</component>
- <inverse>hadRevision</inverse>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Revision"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedRevision"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedRevision"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
- <owl:Axiom>
- <rdfs:comment>Revision is a derivation (see http://www.w3.org/TR/prov-dm/#term-Revision). Moreover, according to
-http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#term-Revision 23 April 2012 'wasRevisionOf is a strict sub-relation of wasDerivedFrom since two entities e2 and e1 may satisfy wasDerivedFrom(e2,e1) without being a variant of each other.'</rdfs:comment>
- <owl:annotatedProperty rdf:resource="&rdfs;subPropertyOf"/>
- <owl:annotatedTarget rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- <owl:annotatedSource rdf:resource="http://www.w3.org/ns/prov#wasRevisionOf"/>
- </owl:Axiom>
-
-
-
- <!-- http://www.w3.org/ns/prov#wasStartedBy -->
-
- <owl:ObjectProperty rdf:about="http://www.w3.org/ns/prov#wasStartedBy">
- <rdfs:label>wasStartedBy</rdfs:label>
- <inverse>started</inverse>
- <category>expanded</category>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">Start is when an activity is deemed to have started. A start may refer to an entity, known as trigger, that initiated the activity.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <rdfs:range rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#qualifiedStart"/>
- <rdfs:subPropertyOf rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- <owl:propertyChainAxiom rdf:parseType="Collection">
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#qualifiedStart"/>
- <rdf:Description rdf:about="http://www.w3.org/ns/prov#entity"/>
- </owl:propertyChainAxiom>
- </owl:ObjectProperty>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Data properties
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/ns/prov#atTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#atTime">
- <rdfs:label>atTime</rdfs:label>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">The time at which an InstantaneousEvent occurred, in the form of xsd:dateTime.</rdfs:comment>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <sharesDefinitionWith rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#endedAtTime"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#generatedAtTime"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#invalidatedAtTime"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#startedAtTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#endedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#endedAtTime">
- <rdfs:label>endedAtTime</rdfs:label>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedEnd o prov:atTime) rdfs:subPropertyOf prov:endedAtTime.</editorialNote>
- <rdfs:comment xml:lang="en">The time at which an activity ended. See also prov:startedAtTime.</rdfs:comment>
- <category>starting-point</category>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#End"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#generatedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#generatedAtTime">
- <rdfs:label>generatedAtTime</rdfs:label>
- <category>expanded</category>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedGeneration o prov:atTime) rdfs:subPropertyOf prov:generatedAtTime.</editorialNote>
- <rdfs:comment xml:lang="en">The time at which an entity was completely created and is available for use.</rdfs:comment>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Generation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#invalidatedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#invalidatedAtTime">
- <rdfs:label>invalidatedAtTime</rdfs:label>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedInvalidation o prov:atTime) rdfs:subPropertyOf prov:invalidatedAtTime.</editorialNote>
- <category>expanded</category>
- <rdfs:comment xml:lang="en">The time at which an entity was invalidated (i.e., no longer usable).</rdfs:comment>
- <component>entities-activities</component>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Invalidation"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#startedAtTime -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#startedAtTime">
- <rdfs:label>startedAtTime</rdfs:label>
- <category>starting-point</category>
- <editorialNote xml:lang="en">It is the intent that the property chain holds: (prov:qualifiedStart o prov:atTime) rdfs:subPropertyOf prov:startedAtTime.</editorialNote>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">The time at which an activity started. See also prov:endedAtTime.</rdfs:comment>
- <rdfs:range rdf:resource="&xsd;dateTime"/>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Activity"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#Start"/>
- <qualifiedForm rdf:resource="http://www.w3.org/ns/prov#atTime"/>
- </owl:DatatypeProperty>
-
-
-
- <!-- http://www.w3.org/ns/prov#value -->
-
- <owl:DatatypeProperty rdf:about="http://www.w3.org/ns/prov#value">
- <rdfs:label>value</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-value</dm>
- <category>expanded</category>
- <editorialNote>The editor's definition comes from http://www.w3.org/TR/rdf-primer/#rdfvalue</editorialNote>
- <definition xml:lang="en">Provides a value that is a direct representation of an entity.</definition>
- <component>entities-activities</component>
- <editorialNote xml:lang="en">This property serves the same purpose as rdf:value, but has been reintroduced to avoid some of the definitional ambiguity in the RDF specification (specifically, 'may be used in describing structured values').</editorialNote>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:domain rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- </owl:DatatypeProperty>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Classes
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/2002/07/owl#Thing -->
-
- <owl:Class rdf:about="&owl;Thing"/>
-
-
-
- <!-- http://www.w3.org/ns/prov#Activity -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Activity">
- <rdfs:label>Activity</rdfs:label>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Activity</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Activity</n>
- <component>entities-activities</component>
- <category>starting-point</category>
- <definition>An activity is something that occurs over a period of time and acts upon or with entities; it may include consuming, processing, transforming, modifying, relocating, using, or generating entities.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#ActivityInfluence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#ActivityInfluence">
- <rdfs:label>ActivityInfluence</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <rdfs:subClassOf>
- <owl:Restriction>
- <owl:onProperty rdf:resource="http://www.w3.org/ns/prov#hadActivity"/>
- <owl:maxCardinality rdf:datatype="&xsd;nonNegativeInteger">0</owl:maxCardinality>
- </owl:Restriction>
- </rdfs:subClassOf>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <editorsDefinition xml:lang="en">ActivitiyInfluence is the capacity of an activity to have an effect on the character, development, or behavior of another by means of generation, invalidation, communication, or other.</editorsDefinition>
- <rdfs:comment xml:lang="en">ActivityInfluence provides additional descriptions of an Activity's binary influence upon any other kind of resource. Instances of ActivityInfluence use the prov:activity property to cite the influencing Activity.</rdfs:comment>
- <rdfs:comment xml:lang="en">It is not recommended that the type ActivityInfluence be asserted without also asserting one of its more specific subclasses.</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#activity"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Agent -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Agent">
- <rdfs:label>Agent</rdfs:label>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Agent</n>
- <definition xml:lang="en">An agent is something that bears some form of responsibility for an activity taking place, for the existence of an entity, or for another agent's activity. </definition>
- <category>starting-point</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#AgentInfluence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#AgentInfluence">
- <rdfs:label>AgentInfluence</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <editorsDefinition xml:lang="en">AgentInfluence is the capacity of an agent to have an effect on the character, development, or behavior of another by means of attribution, association, delegation, or other.</editorsDefinition>
- <rdfs:comment xml:lang="en">AgentInfluence provides additional descriptions of an Agent's binary influence upon any other kind of resource. Instances of AgentInfluence use the prov:agent property to cite the influencing Agent.</rdfs:comment>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">It is not recommended that the type AgentInfluence be asserted without also asserting one of its more specific subclasses.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#agent"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Association -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Association">
- <rdfs:label>Association</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association</n>
- <component>agents-responsibility</component>
- <rdfs:comment xml:lang="en">An instance of prov:Association provides additional descriptions about the binary prov:wasAssociatedWith relation from an prov:Activity to some prov:Agent that had some responsiblity for it. For example, :baking prov:wasAssociatedWith :baker; prov:qualifiedAssociation [ a prov:Association; prov:agent :baker; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <definition xml:lang="en">An activity association is an assignment of responsibility to an agent for an activity, indicating that the agent had a role in the activity. It further allows for a plan to be specified, which is the plan intended by the agent to achieve some goals in the context of this activity.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAssociatedWith"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Attribution -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Attribution">
- <rdfs:label>Attribution</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribution</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribution</n>
- <rdfs:comment xml:lang="en">An instance of prov:Attribution provides additional descriptions about the binary prov:wasAttributedTo relation from an prov:Entity to some prov:Agent that had some responsible for it. For example, :cake prov:wasAttributedTo :baker; prov:qualifiedAttribution [ a prov:Attribution; prov:entity :baker; :foo :bar ].</rdfs:comment>
- <definition xml:lang="en">Attribution is the ascribing of an entity to an agent.
-
-When an entity e is attributed to agent ag, entity e was generated by some unspecified activity that in turn was associated to agent ag. Thus, this relation is useful when the activity is not known, or irrelevant.</definition>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasAttributedTo"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Bundle -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Bundle">
- <rdfs:label>Bundle</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-bundle-entity</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-bundle-declaration</n>
- <category>expanded</category>
- <definition xml:lang="en">A bundle is a named set of provenance descriptions, and is itself an Entity, so allowing provenance of provenance to be expressed.</definition>
- <rdfs:comment xml:lang="en">Note that there are kinds of bundles (e.g. handwritten letters, audio recordings, etc.) that are not expressed in PROV-O, but can be still be described by PROV-O.</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Collection -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Collection">
- <rdfs:label>Collection</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection</dm>
- <component>collections</component>
- <category>expanded</category>
- <definition xml:lang="en">A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Communication -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Communication">
- <rdfs:label>Communication</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Communication</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-wasInformedBy</n>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Communication provides additional descriptions about the binary prov:wasInformedBy relation from an informed prov:Activity to the prov:Activity that informed it. For example, :you_jumping_off_bridge prov:wasInformedBy :everyone_else_jumping_off_bridge; prov:qualifiedCommunication [ a prov:Communication; prov:activity :everyone_else_jumping_off_bridge; :foo :bar ].</rdfs:comment>
- <definition>Communication is the exchange of an entity by two activities, one activity using the entity generated by the other.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInformedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Delegation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Delegation">
- <rdfs:label>Delegation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#AgentInfluence"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-delegation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-delegation</n>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Delegation provides additional descriptions about the binary prov:actedOnBehalfOf relation from a performing prov:Agent to some prov:Agent for whom it was performed. For example, :mixing prov:wasAssociatedWith :toddler . :toddler prov:actedOnBehalfOf :mother; prov:qualifiedDelegation [ a prov:Delegation; prov:entity :mother; :foo :bar ].</rdfs:comment>
- <definition xml:lang="en">Delegation is the assignment of authority and responsibility to an agent (by itself or by another agent) to carry out a specific activity as a delegate or representative, while the agent it acts on behalf of retains some responsibility for the outcome of the delegated work.
-
-For example, a student acted on behalf of his supervisor, who acted on behalf of the department chair, who acted on behalf of the university; all those agents are responsible in some way for the activity that took place but we do not say explicitly who bears responsibility and to what degree.</definition>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#actedOnBehalfOf"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Derivation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Derivation">
- <rdfs:label>Derivation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Derivation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#Derivation-Relation</n>
- <definition xml:lang="en">A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity.</definition>
- <component>derivations</component>
- <rdfs:comment xml:lang="en">An instance of prov:Derivation provides additional descriptions about the binary prov:wasDerivedFrom relation from some derived prov:Entity to another prov:Entity from which it was derived. For example, :chewed_bubble_gum prov:wasDerivedFrom :unwrapped_bubble_gum; prov:qualifiedDerivation [ a prov:Derivation; prov:entity :unwrapped_bubble_gum; :foo :bar ].</rdfs:comment>
- <rdfs:comment xml:lang="en">The more specific forms of prov:Derivation (i.e., prov:Revision, prov:Quotation, prov:PrimarySource) should be asserted if they apply.</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasDerivedFrom"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#EmptyCollection -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#EmptyCollection">
- <rdfs:label xml:lang="en">EmptyCollection</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Collection"/>
- <category>expanded</category>
- <component>collections</component>
- <definition xml:lang="en">An empty collection is a collection without members.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#End -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#End">
- <rdfs:label>End</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-End</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-End</n>
- <rdfs:comment xml:lang="en">An instance of prov:End provides additional descriptions about the binary prov:wasEndedBy relation from some ended prov:Activity to an prov:Entity that ended it. For example, :ball_game prov:wasEndedBy :buzzer; prov:qualifiedEnd [ a prov:End; prov:entity :buzzer; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ].</rdfs:comment>
- <category>qualified</category>
- <definition xml:lang="en">End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger.</definition>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasEndedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Entity -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Entity">
- <rdfs:label>Entity</rdfs:label>
- <owl:disjointWith rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-entity</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Entity</n>
- <component>entities-activities</component>
- <definition xml:lang="en">An entity is a physical, digital, conceptual, or other kind of thing with some fixed aspects; entities may be real or imaginary. </definition>
- <category>starting-point</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#EntityInfluence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#EntityInfluence">
- <rdfs:label>EntityInfluence</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Influence"/>
- <editorsDefinition xml:lang="en">EntityInfluence is the capacity of an entity to have an effect on the character, development, or behavior of another by means of usage, start, end, derivation, or other. </editorsDefinition>
- <rdfs:comment xml:lang="en">EntityInfluence provides additional descriptions of an Entity's binary influence upon any other kind of resource. Instances of EntityInfluence use the prov:entity property to cite the influencing Entity.</rdfs:comment>
- <rdfs:comment xml:lang="en">It is not recommended that the type EntityInfluence be asserted without also asserting one of its more specific subclasses.</rdfs:comment>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#entity"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Generation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Generation">
- <rdfs:label>Generation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Generation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Generation</n>
- <rdfs:comment xml:lang="en">An instance of prov:Generation provides additional descriptions about the binary prov:wasGeneratedBy relation from a generated prov:Entity to the prov:Activity that generated it. For example, :cake prov:wasGeneratedBy :baking; prov:qualifiedGeneration [ a prov:Generation; prov:activity :baking; :foo :bar ].</rdfs:comment>
- <category>qualified</category>
- <component>entities-activities</component>
- <definition xml:lang="en">Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasGeneratedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Influence -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Influence">
- <rdfs:label>Influence</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-influence</n>
- <component>derivations</component>
- <rdfs:comment xml:lang="en">An instance of prov:Influence provides additional descriptions about the binary prov:wasInfluencedBy relation from some influenced Activity, Entity, or Agent to the influencing Activity, Entity, or Agent. For example, :stomach_ache prov:wasInfluencedBy :spoon; prov:qualifiedInfluence [ a prov:Influence; prov:entity :spoon; :foo :bar ] . Because prov:Influence is a broad relation, the more specific relations (Communication, Delegation, End, etc.) should be used when applicable.</rdfs:comment>
- <rdfs:comment xml:lang="en">Because prov:Influence is a broad relation, its most specific subclasses (e.g. prov:Communication, prov:Delegation, prov:End, prov:Revision, etc.) should be used when applicable.</rdfs:comment>
- <category>qualified</category>
- <definition xml:lang="en">Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInfluencedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#InstantaneousEvent -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#InstantaneousEvent">
- <rdfs:label>InstantaneousEvent</rdfs:label>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#dfn-event</constraints>
- <component>entities-activities</component>
- <rdfs:comment xml:lang="en">An instantaneous event, or event for short, happens in the world and marks a change in the world, in its activities and in its entities. The term 'event' is commonly used in process algebra with a similar meaning. Events represent communications or interactions; they are assumed to be atomic and instantaneous.</rdfs:comment>
- <definition xml:lang="en">The PROV data model is implicitly based on a notion of instantaneous events (or just events), that mark transitions in the world. Events include generation, usage, or invalidation of entities, as well as starting or ending of activities. This notion of event is not first-class in the data model, but it is useful for explaining its other concepts and its semantics.</definition>
- <category>qualified</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Invalidation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Invalidation">
- <rdfs:label>Invalidation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#ActivityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Invalidation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Invalidation</n>
- <component>entities-activities</component>
- <definition>Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation.</definition>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Invalidation provides additional descriptions about the binary prov:wasInvalidatedBy relation from an invalidated prov:Entity to the prov:Activity that invalidated it. For example, :uncracked_egg prov:wasInvalidatedBy :baking; prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :baking; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasInvalidatedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Location -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Location">
- <rdfs:label>Location</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-location</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute</n>
- <definition xml:lang="en">A location can be an identifiable geographic place (ISO 19112), but it can also be a non-geographic place such as a directory, row, or column. As such, there are numerous ways in which location can be expressed, such as by a coordinate, address, landmark, and so forth.</definition>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#atLocation"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Organization -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Organization">
- <rdfs:label>Organization</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
- <definition>Agents of type Organization are social institutions such as companies, societies etc.</definition>
- <category>expanded</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Person -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Person">
- <rdfs:label>Person</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
- <category>expanded</category>
- <definition xml:lang="en">Agents of type Person are people.</definition>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Plan -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Plan">
- <rdfs:label>Plan</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Entity"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association</n>
- <definition>A plan is an entity that represents a set of actions or steps intended by one or more agents to achieve some goals.</definition>
- <category>expanded</category>
- <rdfs:comment xml:lang="en">There exist no prescriptive requirement on the nature of plans, their representation, the actions or steps they consist of, or their intended goals. Since plans may evolve over time, it may become necessary to track their provenance, so plans themselves are entities. Representing the plan explicitly in the provenance can be useful for various tasks: for example, to validate the execution as represented in the provenance record, to manage expectation failures, or to provide explanations.</rdfs:comment>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#PrimarySource -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#PrimarySource">
- <rdfs:label>PrimarySource</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-primary-source</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-original-source</n>
- <category>qualified</category>
- <component>derivations</component>
- <definition xml:lang="en">A primary source for a topic refers to something produced by some agent with direct experience and knowledge about the topic, at the time of the topic's study, without benefit from hindsight.
-
-Because of the directness of primary sources, they 'speak for themselves' in ways that cannot be captured through the filter of secondary sources. As such, it is important for secondary sources to reference those primary sources from which they were derived, so that their reliability can be investigated.
-
-A primary source relation is a particular case of derivation of secondary materials from their primary sources. It is recognized that the determination of primary sources can be up to interpretation, and should be done according to conventions accepted within the application's domain.</definition>
- <rdfs:comment xml:lang="en">An instance of prov:PrimarySource provides additional descriptions about the binary prov:hadPrimarySource relation from some secondary prov:Entity to an earlier, primary prov:Entity. For example, :blog prov:hadPrimarySource :newsArticle; prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :newsArticle; :foo :bar ] .</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#hadPrimarySource"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Quotation -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Quotation">
- <rdfs:label>Quotation</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-quotation</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-quotation</n>
- <rdfs:comment xml:lang="en">An instance of prov:Quotation provides additional descriptions about the binary prov:wasQuotedFrom relation from some taken prov:Entity from an earlier, larger prov:Entity. For example, :here_is_looking_at_you_kid prov:wasQuotedFrom :casablanca_script; prov:qualifiedQuotation [ a prov:Quotation; prov:entity :casablanca_script; :foo :bar ].</rdfs:comment>
- <component>derivations</component>
- <category>qualified</category>
- <definition xml:lang="en">A quotation is the repeat of (some or all of) an entity, such as text or image, by someone who may or may not be its original author. Quotation is a particular case of derivation.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasQuotedFrom"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Revision -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Revision">
- <rdfs:label>Revision</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Derivation"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-revision</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Revision</n>
- <component>derivations</component>
- <category>qualified</category>
- <definition xml:lang="en">A revision is a derivation for which the resulting entity is a revised version of some original. The implication here is that the resulting entity contains substantial content from the original. Revision is a particular case of derivation.</definition>
- <rdfs:comment xml:lang="en">An instance of prov:Revision provides additional descriptions about the binary prov:wasRevisionOf relation from some newer prov:Entity to an earlier prov:Entity. For example, :draft_2 prov:wasRevisionOf :draft_1; prov:qualifiedRevision [ a prov:Revision; prov:entity :draft_1; :foo :bar ].</rdfs:comment>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasRevisionOf"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Role -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Role">
- <rdfs:label>Role</rdfs:label>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-role</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute</n>
- <definition xml:lang="en">A role is the function of an entity or agent with respect to an activity, in the context of a usage, generation, invalidation, association, start, and end.</definition>
- <category>qualified</category>
- <component>agents-responsibility</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <rdfs:seeAlso rdf:resource="http://www.w3.org/ns/prov#hadRole"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#SoftwareAgent -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#SoftwareAgent">
- <rdfs:label>SoftwareAgent</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#Agent"/>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types</n>
- <component>agents-responsibility</component>
- <definition xml:lang="en">A software agent is running software.</definition>
- <category>expanded</category>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Start -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Start">
- <rdfs:label>Start</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Start</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Start</n>
- <component>entities-activities</component>
- <category>qualified</category>
- <rdfs:comment xml:lang="en">An instance of prov:Start provides additional descriptions about the binary prov:wasStartedBy relation from some started prov:Activity to an prov:Entity that started it. For example, :foot_race prov:wasStartedBy :bang; prov:qualifiedStart [ a prov:Start; prov:entity :bang; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ] .</rdfs:comment>
- <definition xml:lang="en">Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#wasStartedBy"/>
- </owl:Class>
-
-
-
- <!-- http://www.w3.org/ns/prov#Usage -->
-
- <owl:Class rdf:about="http://www.w3.org/ns/prov#Usage">
- <rdfs:label>Usage</rdfs:label>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#EntityInfluence"/>
- <rdfs:subClassOf rdf:resource="http://www.w3.org/ns/prov#InstantaneousEvent"/>
- <constraints rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig</constraints>
- <dm rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Usage</dm>
- <n rdf:datatype="&xsd;anyURI">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Usage</n>
- <rdfs:comment xml:lang="en">An instance of prov:Usage provides additional descriptions about the binary prov:used relation from some prov:Activity to an prov:Entity that it used. For example, :keynote prov:used :podium; prov:qualifiedUsage [ a prov:Usage; prov:entity :podium; :foo :bar ].</rdfs:comment>
- <definition xml:lang="en">Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity.</definition>
- <category>qualified</category>
- <component>entities-activities</component>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- <unqualifiedForm rdf:resource="http://www.w3.org/ns/prov#used"/>
- </owl:Class>
-
-
-
- <!--
- ///////////////////////////////////////////////////////////////////////////////////////
- //
- // Individuals
- //
- ///////////////////////////////////////////////////////////////////////////////////////
- -->
-
-
-
-
- <!-- http://www.w3.org/ns/prov#EmptyCollection -->
-
- <owl:NamedIndividual rdf:about="http://www.w3.org/ns/prov#EmptyCollection">
- <rdfs:label xml:lang="en">EmptyCollection</rdfs:label>
- <category>expanded</category>
- <component>collections</component>
- <definition xml:lang="en">An empty collection is a collection without members.</definition>
- <rdfs:isDefinedBy rdf:resource="http://www.w3.org/ns/prov#"/>
- </owl:NamedIndividual>
-</rdf:RDF>
-
-
-
-<!-- Generated by the OWL API (version 3.1.0.20069) http://owlapi.sourceforge.net -->
-
--- a/ontology/releases/FR-prov-o/ns/prov-o.ttl Sun Apr 14 19:43:18 2013 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1321 +0,0 @@
-@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
-@prefix : <http://www.w3.org/ns/prov#> .
-@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
-@prefix owl: <http://www.w3.org/2002/07/owl#> .
-@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
-
-rdfs:comment
- a owl:AnnotationProperty ;
- rdfs:comment ""@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-rdfs:isDefinedBy
- a owl:AnnotationProperty .
-
-rdfs:label
- a owl:AnnotationProperty ;
- rdfs:comment ""@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-rdfs:seeAlso
- a owl:AnnotationProperty ;
- rdfs:comment ""@en .
-
-owl:Thing
- a owl:Class .
-
-owl:versionInfo
- a owl:AnnotationProperty .
-
-<http://www.w3.org/ns/prov#>
- a owl:Ontology .
-
-:Activity
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Activity" ;
- owl:disjointWith :Entity ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "An activity is something that occurs over a period of time and acts upon or with entities; it may include consuming, processing, transforming, modifying, relocating, using, or generating entities." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Activity"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Activity"^^xsd:anyURI .
-
-:ActivityInfluence
- a owl:Class ;
- rdfs:comment "ActivityInfluence provides additional descriptions of an Activity's binary influence upon any other kind of resource. Instances of ActivityInfluence use the prov:activity property to cite the influencing Activity."@en, "It is not recommended that the type ActivityInfluence be asserted without also asserting one of its more specific subclasses."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "ActivityInfluence" ;
- rdfs:seeAlso :activity ;
- rdfs:subClassOf :Influence, [
- a owl:Restriction ;
- owl:maxCardinality "0"^^xsd:nonNegativeInteger ;
- owl:onProperty :hadActivity
- ] ;
- owl:disjointWith :EntityInfluence ;
- :category "qualified" ;
- :editorsDefinition "ActivitiyInfluence is the capacity of an activity to have an effect on the character, development, or behavior of another by means of generation, invalidation, communication, or other."@en .
-
-:Agent
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Agent" ;
- owl:disjointWith :InstantaneousEvent ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :definition "An agent is something that bears some form of responsibility for an activity taking place, for the existence of an entity, or for another agent's activity. "@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Agent"^^xsd:anyURI .
-
-:AgentInfluence
- a owl:Class ;
- rdfs:comment "AgentInfluence provides additional descriptions of an Agent's binary influence upon any other kind of resource. Instances of AgentInfluence use the prov:agent property to cite the influencing Agent."@en, "It is not recommended that the type AgentInfluence be asserted without also asserting one of its more specific subclasses."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "AgentInfluence" ;
- rdfs:seeAlso :agent ;
- rdfs:subClassOf :Influence ;
- :category "qualified" ;
- :editorsDefinition "AgentInfluence is the capacity of an agent to have an effect on the character, development, or behavior of another by means of attribution, association, delegation, or other."@en .
-
-:Association
- a owl:Class ;
- rdfs:comment "An instance of prov:Association provides additional descriptions about the binary prov:wasAssociatedWith relation from an prov:Activity to some prov:Agent that had some responsiblity for it. For example, :baking prov:wasAssociatedWith :baker; prov:qualifiedAssociation [ a prov:Association; prov:agent :baker; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Association" ;
- rdfs:subClassOf :AgentInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :definition "An activity association is an assignment of responsibility to an agent for an activity, indicating that the agent had a role in the activity. It further allows for a plan to be specified, which is the plan intended by the agent to achieve some goals in the context of this activity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association"^^xsd:anyURI ;
- :unqualifiedForm :wasAssociatedWith .
-
-:Attribution
- a owl:Class ;
- rdfs:comment "An instance of prov:Attribution provides additional descriptions about the binary prov:wasAttributedTo relation from an prov:Entity to some prov:Agent that had some responsible for it. For example, :cake prov:wasAttributedTo :baker; prov:qualifiedAttribution [ a prov:Attribution; prov:entity :baker; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Attribution" ;
- rdfs:subClassOf :AgentInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition """Attribution is the ascribing of an entity to an agent.
-
-When an entity e is attributed to agent ag, entity e was generated by some unspecified activity that in turn was associated to agent ag. Thus, this relation is useful when the activity is not known, or irrelevant."""@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribution"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribution"^^xsd:anyURI ;
- :unqualifiedForm :wasAttributedTo .
-
-:Bundle
- a owl:Class ;
- rdfs:comment "Note that there are kinds of bundles (e.g. handwritten letters, audio recordings, etc.) that are not expressed in PROV-O, but can be still be described by PROV-O."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Bundle" ;
- rdfs:subClassOf :Entity ;
- :category "expanded" ;
- :definition "A bundle is a named set of provenance descriptions, and is itself an Entity, so allowing provenance of provenance to be expressed."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-bundle-entity"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-bundle-declaration"^^xsd:anyURI .
-
-:Collection
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Collection" ;
- rdfs:subClassOf :Entity ;
- :category "expanded" ;
- :component "collections" ;
- :definition "A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection"^^xsd:anyURI .
-
-:Communication
- a owl:Class ;
- rdfs:comment "An instance of prov:Communication provides additional descriptions about the binary prov:wasInformedBy relation from an informed prov:Activity to the prov:Activity that informed it. For example, :you_jumping_off_bridge prov:wasInformedBy :everyone_else_jumping_off_bridge; prov:qualifiedCommunication [ a prov:Communication; prov:activity :everyone_else_jumping_off_bridge; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Communication" ;
- rdfs:subClassOf :ActivityInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Communication is the exchange of an entity by two activities, one activity using the entity generated by the other." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Communication"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-wasInformedBy"^^xsd:anyURI ;
- :unqualifiedForm :wasInformedBy .
-
-:Delegation
- a owl:Class ;
- rdfs:comment "An instance of prov:Delegation provides additional descriptions about the binary prov:actedOnBehalfOf relation from a performing prov:Agent to some prov:Agent for whom it was performed. For example, :mixing prov:wasAssociatedWith :toddler . :toddler prov:actedOnBehalfOf :mother; prov:qualifiedDelegation [ a prov:Delegation; prov:entity :mother; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Delegation" ;
- rdfs:subClassOf :AgentInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :definition """Delegation is the assignment of authority and responsibility to an agent (by itself or by another agent) to carry out a specific activity as a delegate or representative, while the agent it acts on behalf of retains some responsibility for the outcome of the delegated work.
-
-For example, a student acted on behalf of his supervisor, who acted on behalf of the department chair, who acted on behalf of the university; all those agents are responsible in some way for the activity that took place but we do not say explicitly who bears responsibility and to what degree."""@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-delegation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-delegation"^^xsd:anyURI ;
- :unqualifiedForm :actedOnBehalfOf .
-
-:Derivation
- a owl:Class ;
- rdfs:comment "An instance of prov:Derivation provides additional descriptions about the binary prov:wasDerivedFrom relation from some derived prov:Entity to another prov:Entity from which it was derived. For example, :chewed_bubble_gum prov:wasDerivedFrom :unwrapped_bubble_gum; prov:qualifiedDerivation [ a prov:Derivation; prov:entity :unwrapped_bubble_gum; :foo :bar ]."@en, "The more specific forms of prov:Derivation (i.e., prov:Revision, prov:Quotation, prov:PrimarySource) should be asserted if they apply."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Derivation" ;
- rdfs:subClassOf :EntityInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Derivation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#Derivation-Relation"^^xsd:anyURI ;
- :unqualifiedForm :wasDerivedFrom .
-
-:EmptyCollection
- a owl:Class, owl:NamedIndividual ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "EmptyCollection"@en ;
- rdfs:subClassOf :Collection ;
- :category "expanded" ;
- :component "collections" ;
- :definition "An empty collection is a collection without members."@en .
-
-:End
- a owl:Class ;
- rdfs:comment "An instance of prov:End provides additional descriptions about the binary prov:wasEndedBy relation from some ended prov:Activity to an prov:Entity that ended it. For example, :ball_game prov:wasEndedBy :buzzer; prov:qualifiedEnd [ a prov:End; prov:entity :buzzer; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "End" ;
- rdfs:subClassOf :EntityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "End is when an activity is deemed to have been ended by an entity, known as trigger. The activity no longer exists after its end. Any usage, generation, or invalidation involving an activity precedes the activity's end. An end may refer to a trigger entity that terminated the activity, or to an activity, known as ender that generated the trigger."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-End"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-End"^^xsd:anyURI ;
- :unqualifiedForm :wasEndedBy .
-
-:Entity
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Entity" ;
- owl:disjointWith :InstantaneousEvent ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "An entity is a physical, digital, conceptual, or other kind of thing with some fixed aspects; entities may be real or imaginary. "@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-entity"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Entity"^^xsd:anyURI .
-
-:EntityInfluence
- a owl:Class ;
- rdfs:comment "EntityInfluence provides additional descriptions of an Entity's binary influence upon any other kind of resource. Instances of EntityInfluence use the prov:entity property to cite the influencing Entity."@en, "It is not recommended that the type EntityInfluence be asserted without also asserting one of its more specific subclasses."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "EntityInfluence" ;
- rdfs:seeAlso :entity ;
- rdfs:subClassOf :Influence ;
- :category "qualified" ;
- :editorsDefinition "EntityInfluence is the capacity of an entity to have an effect on the character, development, or behavior of another by means of usage, start, end, derivation, or other. "@en .
-
-:Generation
- a owl:Class ;
- rdfs:comment "An instance of prov:Generation provides additional descriptions about the binary prov:wasGeneratedBy relation from a generated prov:Entity to the prov:Activity that generated it. For example, :cake prov:wasGeneratedBy :baking; prov:qualifiedGeneration [ a prov:Generation; prov:activity :baking; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Generation" ;
- rdfs:subClassOf :ActivityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Generation is the completion of production of a new entity by an activity. This entity did not exist before generation and becomes available for usage after this generation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Generation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Generation"^^xsd:anyURI ;
- :unqualifiedForm :wasGeneratedBy .
-
-:Influence
- a owl:Class ;
- rdfs:comment "An instance of prov:Influence provides additional descriptions about the binary prov:wasInfluencedBy relation from some influenced Activity, Entity, or Agent to the influencing Activity, Entity, or Agent. For example, :stomach_ache prov:wasInfluencedBy :spoon; prov:qualifiedInfluence [ a prov:Influence; prov:entity :spoon; :foo :bar ] . Because prov:Influence is a broad relation, the more specific relations (Communication, Delegation, End, etc.) should be used when applicable."@en, "Because prov:Influence is a broad relation, its most specific subclasses (e.g. prov:Communication, prov:Delegation, prov:End, prov:Revision, etc.) should be used when applicable."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Influence" ;
- :category "qualified" ;
- :component "derivations" ;
- :definition "Influence is the capacity of an entity, activity, or agent to have an effect on the character, development, or behavior of another by means of usage, start, end, generation, invalidation, communication, derivation, attribution, association, or delegation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-influence"^^xsd:anyURI ;
- :unqualifiedForm :wasInfluencedBy .
-
-:InstantaneousEvent
- a owl:Class ;
- rdfs:comment "An instantaneous event, or event for short, happens in the world and marks a change in the world, in its activities and in its entities. The term 'event' is commonly used in process algebra with a similar meaning. Events represent communications or interactions; they are assumed to be atomic and instantaneous."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "InstantaneousEvent" ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#dfn-event"^^xsd:anyURI ;
- :definition "The PROV data model is implicitly based on a notion of instantaneous events (or just events), that mark transitions in the world. Events include generation, usage, or invalidation of entities, as well as starting or ending of activities. This notion of event is not first-class in the data model, but it is useful for explaining its other concepts and its semantics."@en .
-
-:Invalidation
- a owl:Class ;
- rdfs:comment "An instance of prov:Invalidation provides additional descriptions about the binary prov:wasInvalidatedBy relation from an invalidated prov:Entity to the prov:Activity that invalidated it. For example, :uncracked_egg prov:wasInvalidatedBy :baking; prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :baking; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Invalidation" ;
- rdfs:subClassOf :ActivityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Invalidation is the start of the destruction, cessation, or expiry of an existing entity by an activity. The entity is no longer available for use (or further invalidation) after invalidation. Any generation or usage of an entity precedes its invalidation." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Invalidation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Invalidation"^^xsd:anyURI ;
- :unqualifiedForm :wasInvalidatedBy .
-
-:Location
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Location" ;
- rdfs:seeAlso :atLocation ;
- :category "expanded" ;
- :definition "A location can be an identifiable geographic place (ISO 19112), but it can also be a non-geographic place such as a directory, row, or column. As such, there are numerous ways in which location can be expressed, such as by a coordinate, address, landmark, and so forth."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-location"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute"^^xsd:anyURI .
-
-:Organization
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Organization" ;
- rdfs:subClassOf :Agent ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :definition "Agents of type Organization are social institutions such as companies, societies etc." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types"^^xsd:anyURI .
-
-:Person
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Person" ;
- rdfs:subClassOf :Agent ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :definition "Agents of type Person are people."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types"^^xsd:anyURI .
-
-:Plan
- a owl:Class ;
- rdfs:comment "There exist no prescriptive requirement on the nature of plans, their representation, the actions or steps they consist of, or their intended goals. Since plans may evolve over time, it may become necessary to track their provenance, so plans themselves are entities. Representing the plan explicitly in the provenance can be useful for various tasks: for example, to validate the execution as represented in the provenance record, to manage expectation failures, or to provide explanations."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Plan" ;
- rdfs:subClassOf :Entity ;
- :category "expanded", "qualified" ;
- :component "agents-responsibility" ;
- :definition "A plan is an entity that represents a set of actions or steps intended by one or more agents to achieve some goals." ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Association"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Association"^^xsd:anyURI .
-
-:PrimarySource
- a owl:Class ;
- rdfs:comment "An instance of prov:PrimarySource provides additional descriptions about the binary prov:hadPrimarySource relation from some secondary prov:Entity to an earlier, primary prov:Entity. For example, :blog prov:hadPrimarySource :newsArticle; prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :newsArticle; :foo :bar ] ."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "PrimarySource" ;
- rdfs:subClassOf :Derivation ;
- :category "qualified" ;
- :component "derivations" ;
- :definition """A primary source for a topic refers to something produced by some agent with direct experience and knowledge about the topic, at the time of the topic's study, without benefit from hindsight.
-
-Because of the directness of primary sources, they 'speak for themselves' in ways that cannot be captured through the filter of secondary sources. As such, it is important for secondary sources to reference those primary sources from which they were derived, so that their reliability can be investigated.
-
-A primary source relation is a particular case of derivation of secondary materials from their primary sources. It is recognized that the determination of primary sources can be up to interpretation, and should be done according to conventions accepted within the application's domain."""@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-primary-source"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-original-source"^^xsd:anyURI ;
- :unqualifiedForm :hadPrimarySource .
-
-:Quotation
- a owl:Class ;
- rdfs:comment "An instance of prov:Quotation provides additional descriptions about the binary prov:wasQuotedFrom relation from some taken prov:Entity from an earlier, larger prov:Entity. For example, :here_is_looking_at_you_kid prov:wasQuotedFrom :casablanca_script; prov:qualifiedQuotation [ a prov:Quotation; prov:entity :casablanca_script; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Quotation" ;
- rdfs:subClassOf :Derivation ;
- :category "qualified" ;
- :component "derivations" ;
- :definition "A quotation is the repeat of (some or all of) an entity, such as text or image, by someone who may or may not be its original author. Quotation is a particular case of derivation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-quotation"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-quotation"^^xsd:anyURI ;
- :unqualifiedForm :wasQuotedFrom .
-
-:Revision
- a owl:Class ;
- rdfs:comment "An instance of prov:Revision provides additional descriptions about the binary prov:wasRevisionOf relation from some newer prov:Entity to an earlier prov:Entity. For example, :draft_2 prov:wasRevisionOf :draft_1; prov:qualifiedRevision [ a prov:Revision; prov:entity :draft_1; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Revision" ;
- rdfs:subClassOf :Derivation ;
- :category "qualified" ;
- :component "derivations" ;
- :definition "A revision is a derivation for which the resulting entity is a revised version of some original. The implication here is that the resulting entity contains substantial content from the original. Revision is a particular case of derivation."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-revision"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Revision"^^xsd:anyURI ;
- :unqualifiedForm :wasRevisionOf .
-
-:Role
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Role" ;
- rdfs:seeAlso :hadRole ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :definition "A role is the function of an entity or agent with respect to an activity, in the context of a usage, generation, invalidation, association, start, and end."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-role"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-attribute"^^xsd:anyURI .
-
-:SoftwareAgent
- a owl:Class ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "SoftwareAgent" ;
- rdfs:subClassOf :Agent ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :definition "A software agent is running software."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-agent"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-types"^^xsd:anyURI .
-
-:Start
- a owl:Class ;
- rdfs:comment "An instance of prov:Start provides additional descriptions about the binary prov:wasStartedBy relation from some started prov:Activity to an prov:Entity that started it. For example, :foot_race prov:wasStartedBy :bang; prov:qualifiedStart [ a prov:Start; prov:entity :bang; :foo :bar; prov:atTime '2012-03-09T08:05:08-05:00'^^xsd:dateTime ] ."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Start" ;
- rdfs:subClassOf :EntityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Start is when an activity is deemed to have been started by an entity, known as trigger. The activity did not exist before its start. Any usage, generation, or invalidation involving an activity follows the activity's start. A start may refer to a trigger entity that set off the activity, or to an activity, known as starter, that generated the trigger."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Start"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Start"^^xsd:anyURI ;
- :unqualifiedForm :wasStartedBy .
-
-:Usage
- a owl:Class ;
- rdfs:comment "An instance of prov:Usage provides additional descriptions about the binary prov:used relation from some prov:Activity to an prov:Entity that it used. For example, :keynote prov:used :podium; prov:qualifiedUsage [ a prov:Usage; prov:entity :podium; :foo :bar ]."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "Usage" ;
- rdfs:subClassOf :EntityInfluence, :InstantaneousEvent ;
- :category "qualified" ;
- :component "entities-activities" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Usage is the beginning of utilizing an entity by an activity. Before usage, the activity had not begun to utilize this entity and could not have been affected by the entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-Usage"^^xsd:anyURI ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-Usage"^^xsd:anyURI ;
- :unqualifiedForm :used .
-
-:actedOnBehalfOf
- a owl:ObjectProperty ;
- rdfs:comment "An object property to express the accountability of an agent towards another agent. The subordinate agent acted on behalf of the responsible agent in an actual activity. "@en ;
- rdfs:domain :Agent ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "actedOnBehalfOf" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedDelegation
- :agent
- ) ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :inverse "hadDelegate" ;
- :qualifiedForm :Delegation, :qualifiedDelegation .
-
-:activity
- a owl:ObjectProperty ;
- rdfs:domain :ActivityInfluence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "activity" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :influencer ;
- :category "qualified" ;
- :editorialNote "This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple."@en ;
- :editorsDefinition "The prov:activity property references an prov:Activity which influenced a resource. This property applies to an prov:ActivityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent." ;
- :inverse "activityOfInfluence" .
-
-:agent
- a owl:ObjectProperty ;
- rdfs:domain :AgentInfluence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "agent" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :influencer ;
- :category "qualified" ;
- :editorialNote "This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple."@en ;
- :editorsDefinition "The prov:agent property references an prov:Agent which influenced a resource. This property applies to an prov:AgentInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent."@en ;
- :inverse "agentOfInfluence" .
-
-:alternateOf
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "alternateOf" ;
- rdfs:range :Entity ;
- rdfs:seeAlso :specializationOf ;
- :category "expanded" ;
- :component "alternate" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "Two alternate entities present aspects of the same thing. These aspects may be the same or different, and the alternate entities may or may not overlap in time."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-alternate"^^xsd:anyURI ;
- :inverse "alternateOf" ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-alternate"^^xsd:anyURI .
-
-:aq
- a owl:AnnotationProperty ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:atLocation
- a owl:ObjectProperty ;
- rdfs:comment "The Location of any resource."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- :InstantaneousEvent
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "atLocation" ;
- rdfs:range :Location ;
- :category "expanded" ;
- :editorialNote "The naming of prov:atLocation parallels prov:atTime, and is not named prov:hadLocation to avoid conflicting with the convention that prov:had* properties are used on prov:Influence classes."@en, "This property is not functional because the many values could be at a variety of granularies (In this building, in this room, in that chair)."@en ;
- :inverse "locationOf" ;
- :sharesDefinitionWith :Location .
-
-:atTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an InstantaneousEvent occurred, in the form of xsd:dateTime."@en ;
- rdfs:domain :InstantaneousEvent ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "atTime" ;
- rdfs:range xsd:dateTime ;
- :category "qualified" ;
- :component "entities-activities" ;
- :sharesDefinitionWith :InstantaneousEvent ;
- :unqualifiedForm :endedAtTime, :generatedAtTime, :invalidatedAtTime, :startedAtTime .
-
-:category
- a owl:AnnotationProperty ;
- rdfs:comment "Classify prov-o terms into three categories, including 'starting-point', 'qualifed', and 'extended'. This classification is used by the prov-o html document to gently introduce prov-o terms to its users. "@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:component
- a owl:AnnotationProperty ;
- rdfs:comment "Classify prov-o terms into six components according to prov-dm, including 'agents-responsibility', 'alternate', 'annotations', 'collections', 'derivations', and 'entities-activities'. This classification is used so that readers of prov-o specification can find its correspondence with the prov-dm specification."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:constraints
- a owl:AnnotationProperty ;
- rdfs:comment "A reference to the principal section of the PROV-CONSTRAINTS document that describes this concept."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:definition
- a owl:AnnotationProperty ;
- rdfs:comment "A definition quoted from PROV-DM or PROV-CONSTRAINTS that describes the concept expressed with this OWL term."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:dm
- a owl:AnnotationProperty ;
- rdfs:comment "A reference to the principal section of the PROV-DM document that describes this concept."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:editorialNote
- a owl:AnnotationProperty ;
- rdfs:comment "A note by the OWL development team about how this term expresses the PROV-DM concept, or how it should be used in context of semantic web or linked data."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:editorsDefinition
- a owl:AnnotationProperty ;
- rdfs:comment "When the prov-o term does not have a definition drawn from prov-dm, and the prov-o editor provides one."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf :definition .
-
-:endedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an activity ended. See also prov:startedAtTime."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "endedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedEnd o prov:atTime) rdfs:subPropertyOf prov:endedAtTime."@en ;
- :qualifiedForm :End, :atTime .
-
-:entity
- a owl:ObjectProperty ;
- rdfs:domain :EntityInfluence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "entity" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :influencer ;
- :category "qualified" ;
- :editorialNote "This property behaves in spirit like rdf:object; it references the object of a prov:wasInfluencedBy triple."@en ;
- :editorsDefinition "The prov:entity property references an prov:Entity which influenced a resource. This property applies to an prov:EntityInfluence, which is given by a subproperty of prov:qualifiedInfluence from the influenced prov:Entity, prov:Activity or prov:Agent." ;
- :inverse "entityOfInfluence" .
-
-:generated
- a owl:ObjectProperty ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "generated" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :influenced ;
- owl:inverseOf :wasGeneratedBy ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "prov:generated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions."@en ;
- :inverse "wasGeneratedBy" ;
- :sharesDefinitionWith :Generation .
-
-:generatedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an entity was completely created and is available for use."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "generatedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedGeneration o prov:atTime) rdfs:subPropertyOf prov:generatedAtTime."@en ;
- :qualifiedForm :Generation, :atTime .
-
-:hadActivity
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Activity of an Influence, which used, generated, invalidated, or was the responsibility of some Entity. This property is _not_ used by ActivityInfluence (use prov:activity instead)."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain :Influence, [
- a owl:Class ;
- owl:unionOf (:Delegation
- :Derivation
- :End
- :Start
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadActivity" ;
- rdfs:range :Activity ;
- :category "qualified" ;
- :component "derivations" ;
- :editorialNote "The multiple rdfs:domain assertions are intended. One is simpler and works for OWL-RL, the union is more specific but is not recognized by OWL-RL."@en ;
- :inverse "wasActivityOfInfluence" ;
- :sharesDefinitionWith :Activity .
-
-:hadGeneration
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Generation involved in an Entity's Derivation."@en ;
- rdfs:domain :Derivation ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadGeneration" ;
- rdfs:range :Generation ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "generatedAsDerivation" ;
- :sharesDefinitionWith :Generation .
-
-:hadMember
- a owl:ObjectProperty ;
- rdfs:domain :Collection ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadMember" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- :category "expanded" ;
- :component "expanded" ;
- :inverse "wasMemberOf" ;
- :sharesDefinitionWith :Collection .
-
-:hadPlan
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Plan adopted by an Agent in Association with some Activity. Plan specifications are out of the scope of this specification."@en ;
- rdfs:domain :Association ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadPlan" ;
- rdfs:range :Plan ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "wasPlanOf" ;
- :sharesDefinitionWith :Plan .
-
-:hadPrimarySource
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadPrimarySource" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasDerivedFrom ;
- owl:propertyChainAxiom (:qualifiedPrimarySource
- :entity
- ) ;
- :category "expanded" ;
- :component "derivations" ;
- :inverse "wasPrimarySourceOf" ;
- :qualifiedForm :PrimarySource, :qualifiedPrimarySource .
-
-:hadRole
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Role that an Entity assumed in the context of an Activity. For example, :baking prov:used :spoon; prov:qualified [ a prov:Usage; prov:entity :spoon; prov:hadRole roles:mixing_implement ]."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain :Influence, [
- a owl:Class ;
- owl:unionOf (:Association
- :InstantaneousEvent
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadRole" ;
- rdfs:range :Role ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :editorsDefinition "prov:hadRole references the Role (i.e. the function of an entity with respect to an activity), in the context of an instantaneous usage, generation, association, start, and end."@en ;
- :inverse "wasRoleIn" ;
- :sharesDefinitionWith :Role .
-
-:hadUsage
- a owl:ObjectProperty ;
- rdfs:comment "The _optional_ Usage involved in an Entity's Derivation."@en ;
- rdfs:domain :Derivation ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "hadUsage" ;
- rdfs:range :Usage ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "wasUsedInDerivation" ;
- :sharesDefinitionWith :Usage .
-
-:influenced
- a owl:ObjectProperty ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "influenced" ;
- owl:inverseOf :wasInfluencedBy ;
- :category "expanded" ;
- :component "agents-responsibility" ;
- :inverse "wasInfluencedBy" ;
- :sharesDefinitionWith :Influence .
-
-:influencer
- a owl:ObjectProperty ;
- rdfs:comment "Subproperties of prov:influencer are used to cite the object of an unqualified PROV-O triple whose predicate is a subproperty of prov:wasInfluencedBy (e.g. prov:used, prov:wasGeneratedBy). prov:influencer is used much like rdf:object is used."@en ;
- rdfs:domain :Influence ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "influencer" ;
- rdfs:range owl:Thing ;
- :category "qualified" ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence"^^xsd:anyURI ;
- :editorialNote "This property and its subproperties are used in the same way as the rdf:object property, i.e. to reference the object of an unqualified prov:wasInfluencedBy or prov:influenced triple."@en ;
- :editorsDefinition "This property is used as part of the qualified influence pattern. Subclasses of prov:Influence use these subproperties to reference the resource (Entity, Agent, or Activity) whose influence is being qualified."@en ;
- :inverse "hadInfluence" .
-
-:invalidated
- a owl:ObjectProperty ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "invalidated" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :influenced ;
- owl:inverseOf :wasInvalidatedBy ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "prov:invalidated is one of few inverse property defined, to allow Activity-oriented assertions in addition to Entity-oriented assertions."@en ;
- :inverse "wasInvalidatedBy" ;
- :sharesDefinitionWith :Invalidation .
-
-:invalidatedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an entity was invalidated (i.e., no longer usable)."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "invalidatedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "expanded" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedInvalidation o prov:atTime) rdfs:subPropertyOf prov:invalidatedAtTime."@en ;
- :qualifiedForm :Invalidation, :atTime .
-
-:inverse
- a owl:AnnotationProperty ;
- rdfs:comment "PROV-O does not define all property inverses. The directionalities defined in PROV-O should be given preference over those not defined. However, if users wish to name the inverse of a PROV-O property, the local name given by prov:inverse should be used."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:seeAlso <http://www.w3.org/TR/prov-o/#names-of-inverse-properties> .
-
-:n
- a owl:AnnotationProperty ;
- rdfs:comment "A reference to the principal section of the PROV-DM document that describes this concept."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:order
- a owl:AnnotationProperty ;
- rdfs:comment "The position that this OWL term should be listed within documentation. The scope of the documentation (e.g., among all terms, among terms within a prov:category, among properties applying to a particular class, etc.) is unspecified."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> .
-
-:qualifiedAssociation
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasAssociatedWith Agent :ag, then it can qualify the Association using prov:qualifiedAssociation [ a prov:Association; prov:agent :ag; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedAssociation" ;
- rdfs:range :Association ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "qualifiedAssociationOf" ;
- :sharesDefinitionWith :Association ;
- :unqualifiedForm :wasAssociatedWith .
-
-:qualifiedAttribution
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasAttributedTo Agent :ag, then it can qualify how it was influenced using prov:qualifiedAttribution [ a prov:Attribution; prov:agent :ag; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedAttribution" ;
- rdfs:range :Attribution ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "qualifiedAttributionOf" ;
- :sharesDefinitionWith :Attribution ;
- :unqualifiedForm :wasAttributedTo .
-
-:qualifiedCommunication
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasInformedBy Activity :a, then it can qualify how it was influenced using prov:qualifiedCommunication [ a prov:Communication; prov:activity :a; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedCommunication" ;
- rdfs:range :Communication ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedCommunicationOf" ;
- :qualifiedForm :Communication ;
- :sharesDefinitionWith :Communication .
-
-:qualifiedDelegation
- a owl:ObjectProperty ;
- rdfs:comment "If this Agent prov:actedOnBehalfOf Agent :ag, then it can qualify how with prov:qualifiedResponsibility [ a prov:Responsibility; prov:agent :ag; :foo :bar ]."@en ;
- rdfs:domain :Agent ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedDelegation" ;
- rdfs:range :Delegation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :inverse "qualifiedDelegationOf" ;
- :sharesDefinitionWith :Delegation ;
- :unqualifiedForm :actedOnBehalfOf .
-
-:qualifiedDerivation
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasDerivedFrom Entity :e, then it can qualify how it was derived using prov:qualifiedDerivation [ a prov:Derivation; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedDerivation" ;
- rdfs:range :Derivation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedDerivationOf" ;
- :sharesDefinitionWith :Derivation ;
- :unqualifiedForm :wasDerivedFrom .
-
-:qualifiedEnd
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasEndedBy Entity :e1, then it can qualify how it was ended using prov:qualifiedEnd [ a prov:End; prov:entity :e1; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedEnd" ;
- rdfs:range :End ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedEndOf" ;
- :sharesDefinitionWith :End ;
- :unqualifiedForm :wasEndedBy .
-
-:qualifiedForm
- a owl:AnnotationProperty ;
- rdfs:comment """This annotation property links a subproperty of prov:wasInfluencedBy with the subclass of prov:Influence and the qualifying property that are used to qualify it.
-
-Example annotation:
-
- prov:wasGeneratedBy prov:qualifiedForm prov:qualifiedGeneration, prov:Generation .
-
-Then this unqualified assertion:
-
- :entity1 prov:wasGeneratedBy :activity1 .
-
-can be qualified by adding:
-
- :entity1 prov:qualifiedGeneration :entity1Gen .
- :entity1Gen
- a prov:Generation, prov:Influence;
- prov:activity :activity1;
- :customValue 1337 .
-
-Note how the value of the unqualified influence (prov:wasGeneratedBy :activity1) is mirrored as the value of the prov:activity (or prov:entity, or prov:agent) property on the influence class."""@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:qualifiedGeneration
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:generated Entity :e, then it can qualify how it performed the Generation using prov:qualifiedGeneration [ a prov:Generation; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedGeneration" ;
- rdfs:range :Generation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedGenerationOf" ;
- :sharesDefinitionWith :Generation ;
- :unqualifiedForm :wasGeneratedBy .
-
-:qualifiedInfluence
- a owl:ObjectProperty ;
- rdfs:comment "Because prov:qualifiedInfluence is a broad relation, the more specific relations (qualifiedCommunication, qualifiedDelegation, qualifiedEnd, etc.) should be used when applicable."@en ;
- rdfs:domain [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedInfluence" ;
- rdfs:range :Influence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedInfluenceOf" ;
- :sharesDefinitionWith :Influence ;
- :unqualifiedForm :wasInfluencedBy .
-
-:qualifiedInvalidation
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasInvalidatedBy Activity :a, then it can qualify how it was invalidated using prov:qualifiedInvalidation [ a prov:Invalidation; prov:activity :a; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedInvalidation" ;
- rdfs:range :Invalidation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedInvalidationOf" ;
- :sharesDefinitionWith :Invalidation ;
- :unqualifiedForm :wasInvalidatedBy .
-
-:qualifiedPrimarySource
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:hadPrimarySource Entity :e, then it can qualify how using prov:qualifiedPrimarySource [ a prov:PrimarySource; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedPrimarySource" ;
- rdfs:range :PrimarySource ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedSourceOf" ;
- :sharesDefinitionWith :PrimarySource ;
- :unqualifiedForm :hadPrimarySource .
-
-:qualifiedQuotation
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasQuotedFrom Entity :e, then it can qualify how using prov:qualifiedQuotation [ a prov:Quotation; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedQuotation" ;
- rdfs:range :Quotation ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "qualifiedQuotationOf" ;
- :sharesDefinitionWith :Quotation ;
- :unqualifiedForm :wasQuotedFrom .
-
-:qualifiedRevision
- a owl:ObjectProperty ;
- rdfs:comment "If this Entity prov:wasRevisionOf Entity :e, then it can qualify how it was revised using prov:qualifiedRevision [ a prov:Revision; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedRevision" ;
- rdfs:range :Revision ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "derivations" ;
- :inverse "revisedEntity" ;
- :sharesDefinitionWith :Revision ;
- :unqualifiedForm :wasRevisionOf .
-
-:qualifiedStart
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:wasStartedBy Entity :e1, then it can qualify how it was started using prov:qualifiedStart [ a prov:Start; prov:entity :e1; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedStart" ;
- rdfs:range :Start ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedStartOf" ;
- :sharesDefinitionWith :Start ;
- :unqualifiedForm :wasStartedBy .
-
-:qualifiedUsage
- a owl:ObjectProperty ;
- rdfs:comment "If this Activity prov:used Entity :e, then it can qualify how it used it using prov:qualifiedUsage [ a prov:Usage; prov:entity :e; :foo :bar ]."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "qualifiedUsage" ;
- rdfs:range :Usage ;
- rdfs:subPropertyOf :qualifiedInfluence ;
- :category "qualified" ;
- :component "entities-activities" ;
- :inverse "qualifiedUsingActivity" ;
- :sharesDefinitionWith :Usage ;
- :unqualifiedForm :used .
-
-:sharesDefinitionWith
- a owl:AnnotationProperty ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:specializationOf
- a owl:AnnotationProperty, owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "specializationOf" ;
- rdfs:range :Entity ;
- rdfs:seeAlso :alternateOf ;
- rdfs:subPropertyOf :alternateOf ;
- :category "expanded" ;
- :component "alternate" ;
- :constraints "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#prov-dm-constraints-fig"^^xsd:anyURI ;
- :definition "An entity that is a specialization of another shares all aspects of the latter, and additionally presents more specific aspects of the same thing as the latter. In particular, the lifetime of the entity being specialized contains that of any specialization. Examples of aspects include a time period, an abstraction, and a context associated with the entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-specialization"^^xsd:anyURI ;
- :inverse "generalizationOf" ;
- :n "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-n.html#expression-specialization"^^xsd:anyURI .
-
-:startedAtTime
- a owl:DatatypeProperty ;
- rdfs:comment "The time at which an activity started. See also prov:endedAtTime."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "startedAtTime" ;
- rdfs:range xsd:dateTime ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :editorialNote "It is the intent that the property chain holds: (prov:qualifiedStart o prov:atTime) rdfs:subPropertyOf prov:startedAtTime."@en ;
- :qualifiedForm :Start, :atTime .
-
-:todo
- a owl:AnnotationProperty .
-
-:unqualifiedForm
- a owl:AnnotationProperty ;
- rdfs:comment "Classes and properties used to qualify relationships are annotated with prov:unqualifiedForm to indicate the property used to assert an unqualified provenance relation."@en ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:subPropertyOf rdfs:seeAlso .
-
-:used
- a owl:ObjectProperty ;
- rdfs:comment "A prov:Entity that was used by this prov:Activity. For example, :baking prov:used :spoon, :egg, :oven ."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "used" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedUsage
- :entity
- ) ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :inverse "wasUsedBy" ;
- :qualifiedForm :Usage, :qualifiedUsage .
-
-:value
- a owl:DatatypeProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "value" ;
- :category "expanded" ;
- :component "entities-activities" ;
- :definition "Provides a value that is a direct representation of an entity."@en ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-attribute-value"^^xsd:anyURI ;
- :editorialNote "The editor's definition comes from http://www.w3.org/TR/rdf-primer/#rdfvalue", "This property serves the same purpose as rdf:value, but has been reintroduced to avoid some of the definitional ambiguity in the RDF specification (specifically, 'may be used in describing structured values')."@en .
-
-:wasAssociatedWith
- a owl:ObjectProperty ;
- rdfs:comment "An prov:Agent that had some (unspecified) responsibility for the occurrence of this prov:Activity."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasAssociatedWith" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedAssociation
- :agent
- ) ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :inverse "wasAssociateFor" ;
- :qualifiedForm :Association, :qualifiedAssociation .
-
-:wasAttributedTo
- a owl:ObjectProperty ;
- rdfs:comment "Attribution is the ascribing of an entity to an agent."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasAttributedTo" ;
- rdfs:range :Agent ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedAttribution
- :agent
- ) ;
- :category "starting-point" ;
- :component "agents-responsibility" ;
- :definition "Attribution is the ascribing of an entity to an agent."@en ;
- :inverse "contributed" ;
- :qualifiedForm :Attribution, :qualifiedAttribution .
-
-:wasDerivedFrom
- a owl:ObjectProperty ;
- rdfs:comment "The more specific subproperties of prov:wasDerivedFrom (i.e., prov:wasQuotedFrom, prov:wasRevisionOf, prov:hadPrimarySource) should be used when applicable."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasDerivedFrom" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedDerivation
- :entity
- ) ;
- :category "starting-point" ;
- :component "derivations" ;
- :definition "A derivation is a transformation of an entity into another, an update of an entity resulting in a new one, or the construction of a new entity based on a pre-existing entity."@en ;
- :inverse "hadDerivation" ;
- :qualifiedForm :Derivation, :qualifiedDerivation .
-
-:wasEndedBy
- a owl:ObjectProperty ;
- rdfs:comment "End is when an activity is deemed to have ended. An end may refer to an entity, known as trigger, that terminated the activity."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasEndedBy" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedEnd
- :entity
- ) ;
- :category "expanded" ;
- :component "entities-activities" ;
- :inverse "ended" ;
- :qualifiedForm :End, :qualifiedEnd .
-
-:wasGeneratedBy
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasGeneratedBy" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedGeneration
- :activity
- ) ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :inverse "generated" ;
- :qualifiedForm :Generation, :qualifiedGeneration .
-
-:wasInfluencedBy
- a owl:ObjectProperty ;
- rdfs:comment "Because prov:wasInfluencedBy is a broad relation, its more specific subproperties (e.g. prov:wasInformedBy, prov:actedOnBehalfOf, prov:wasEndedBy, etc.) should be used when applicable."@en, "This property has multiple RDFS domains to suit multiple OWL Profiles. See <a href=\"#owl-profile\">PROV-O OWL Profile</a>." ;
- rdfs:domain [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasInfluencedBy" ;
- rdfs:range [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- :category "qualified" ;
- :component "agents-responsibility" ;
- :editorialNote """The sub-properties of prov:wasInfluencedBy can be elaborated in more detail using the Qualification Pattern. For example, the binary relation :baking prov:used :spoon can be qualified by asserting :baking prov:qualifiedUsage [ a prov:Usage; prov:entity :spoon; prov:atLocation :kitchen ] .
-
-Subproperties of prov:wasInfluencedBy may also be asserted directly without being qualified.
-
-prov:wasInfluencedBy should not be used without also using one of its subproperties.
-"""@en ;
- :inverse "influenced" ;
- :qualifiedForm :Influence, :qualifiedInfluence ;
- :sharesDefinitionWith :Influence .
-
-:wasInformedBy
- a owl:ObjectProperty ;
- rdfs:comment "An activity a2 is dependent on or informed by another activity a1, by way of some unspecified entity that is generated by a1 and used by a2."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasInformedBy" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedCommunication
- :activity
- ) ;
- :category "starting-point" ;
- :component "entities-activities" ;
- :inverse "informed" ;
- :qualifiedForm :Communication, :qualifiedCommunication .
-
-:wasInvalidatedBy
- a owl:ObjectProperty ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasInvalidatedBy" ;
- rdfs:range :Activity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedInvalidation
- :activity
- ) ;
- :category "expanded" ;
- :component "entities-activities" ;
- :inverse "invalidated" ;
- :qualifiedForm :Invalidation, :qualifiedInvalidation .
-
-:wasQuotedFrom
- a owl:ObjectProperty ;
- rdfs:comment "An entity is derived from an original entity by copying, or 'quoting', some or all of it."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasQuotedFrom" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasDerivedFrom ;
- owl:propertyChainAxiom (:qualifiedQuotation
- :entity
- ) ;
- :category "expanded" ;
- :component "derivations" ;
- :inverse "quotedAs" ;
- :qualifiedForm :Quotation, :qualifiedQuotation .
-
-:wasRevisionOf
- a owl:AnnotationProperty, owl:ObjectProperty ;
- rdfs:comment "A revision is a derivation that revises an entity into a revised version."@en ;
- rdfs:domain :Entity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasRevisionOf" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasDerivedFrom ;
- owl:propertyChainAxiom (:qualifiedRevision
- :entity
- ) ;
- :category "expanded" ;
- :component "derivations" ;
- :inverse "hadRevision" ;
- :qualifiedForm :Revision, :qualifiedRevision .
-
-:wasStartedBy
- a owl:ObjectProperty ;
- rdfs:comment "Start is when an activity is deemed to have started. A start may refer to an entity, known as trigger, that initiated the activity."@en ;
- rdfs:domain :Activity ;
- rdfs:isDefinedBy <http://www.w3.org/ns/prov#> ;
- rdfs:label "wasStartedBy" ;
- rdfs:range :Entity ;
- rdfs:subPropertyOf :wasInfluencedBy ;
- owl:propertyChainAxiom (:qualifiedStart
- :entity
- ) ;
- :category "expanded" ;
- :component "entities-activities" ;
- :inverse "started" ;
- :qualifiedForm :Start, :qualifiedStart .
-
-<http://www.w3.org/ns/prov-o#>
- a owl:Ontology ;
- rdfs:comment """This document is published by the Provenance Working Group (http://www.w3.org/2011/prov/wiki/Main_Page).
-
-If you wish to make comments regarding this document, please send them to public-prov-comments@w3.org (subscribe public-prov-comments-request@w3.org, archives http://lists.w3.org/Archives/Public/public-prov-comments/). All feedback is welcome."""@en ;
- rdfs:label "W3C PROVenance Interchange Ontology (PROV-O)"@en ;
- rdfs:seeAlso <http://www.w3.org/TR/prov-o/>, <http://www.w3.org/ns/prov> ;
- owl:versionIRI <http://www.w3.org/ns/prov-o-20130312> ;
- owl:versionInfo "Proposed Recommendation version 2013-03-12"@en ;
- :specializationOf <http://www.w3.org/ns/prov-o> ;
- :wasRevisionOf <http://www.w3.org/ns/prov-o-20121211> .
-
-[]
- a owl:Axiom ;
- rdfs:comment "A collection is an entity that provides a structure to some constituents, which are themselves entities. These constituents are said to be member of the collections."@en ;
- owl:annotatedProperty rdfs:range ;
- owl:annotatedSource :hadMember ;
- owl:annotatedTarget :Entity ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-collection" .
-
-[]
- a owl:Axiom ;
- rdfs:comment "hadPrimarySource property is a particular case of wasDerivedFrom (see http://www.w3.org/TR/prov-dm/#term-original-source) that aims to give credit to the source that originated some information." ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :hadPrimarySource ;
- owl:annotatedTarget :wasDerivedFrom .
-
-[]
- a owl:Axiom ;
- rdfs:comment "Attribution is a particular case of trace (see http://www.w3.org/TR/prov-dm/#concept-trace), in the sense that it links an entity to the agent that ascribed it." ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasAttributedTo ;
- owl:annotatedTarget :wasInfluencedBy ;
- :definition "IF wasAttributedTo(e2,ag1,aAttr) holds, THEN wasInfluencedBy(e2,ag1) also holds. " .
-
-[]
- a owl:Axiom ;
- rdfs:comment "Derivation is a particular case of trace (see http://www.w3.org/TR/prov-dm/#term-trace), since it links an entity to another entity that contributed to its existence." ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasDerivedFrom ;
- owl:annotatedTarget :wasInfluencedBy .
-
-[]
- a owl:Axiom ;
- owl:annotatedProperty rdfs:range ;
- owl:annotatedSource :wasInfluencedBy ;
- owl:annotatedTarget [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- :definition "influencer: an identifier (o1) for an ancestor entity, activity, or agent that the former depends on;" ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence" .
-
-[]
- a owl:Axiom ;
- owl:annotatedProperty rdfs:domain ;
- owl:annotatedSource :wasInfluencedBy ;
- owl:annotatedTarget [
- a owl:Class ;
- owl:unionOf (:Activity
- :Agent
- :Entity
- )
- ] ;
- :definition "influencee: an identifier (o2) for an entity, activity, or agent; " ;
- :dm "http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#term-influence" .
-
-[]
- a owl:Axiom ;
- rdfs:comment "Quotation is a particular case of derivation (see http://www.w3.org/TR/prov-dm/#term-quotation) in which an entity is derived from an original entity by copying, or \"quoting\", some or all of it. " ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasQuotedFrom ;
- owl:annotatedTarget :wasDerivedFrom .
-
-[]
- a owl:Axiom ;
- rdfs:comment """Revision is a derivation (see http://www.w3.org/TR/prov-dm/#term-Revision). Moreover, according to
-http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#term-Revision 23 April 2012 'wasRevisionOf is a strict sub-relation of wasDerivedFrom since two entities e2 and e1 may satisfy wasDerivedFrom(e2,e1) without being a variant of each other.'""" ;
- owl:annotatedProperty rdfs:subPropertyOf ;
- owl:annotatedSource :wasRevisionOf ;
- owl:annotatedTarget :wasDerivedFrom .
-
--- a/ontology/releases/REC-prov-o-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/ontology/releases/REC-prov-o-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -1324,7 +1324,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
@@ -4101,7 +4101,7 @@
</span>
</h3>
<p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Person</p>
- <div class="definition"><p>Agents of type Person are people.</p>
+ <div class="definition"><p>Person agents are people.</p>
</div>
<div class="example">
@@ -4195,7 +4195,7 @@
</span>
</h3>
<p><strong class="crossreference">IRI:</strong>http://www.w3.org/ns/prov#Organization</p>
- <div class="definition"><p>Agents of type Organization are social institutions such as companies, societies etc.</p>
+ <div class="definition"><p>An organization is a social or legal institution such as a company, society, etc.</p>
</div>
<div class="example">
@@ -10446,6 +10446,10 @@
<!--OddPage--><h2><span class="secno">E. </span>Changes since PR-prov-o-20130312</h2><p><em>This section is non-normative.</em></p>
<ul>
<li>Fixed typo in <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/#alternateOf">alternateOf</a> example: <tt>:london_forecast_043</tt> became <tt>:london_forecast_0413</tt></li>
+ <li>Changed capitalization in definitions for
+ <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/#SoftwareAgent">Organization</a> (<a href="#Organization">new</a>) and
+ <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/#SoftwareAgent">Person</a> (<a href="#Person">new</a>).
+ </li>
</ul>
</div>
Binary file overview/prov-family.png has changed
Binary file overview/prov-family.pptx has changed
--- a/overview/prov-overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/overview/prov-overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -298,12 +298,12 @@
berjon.biblio[k] = extraReferences[k];
};
var extraReferences = {
-
+ "PROV-XG" : "Yolanda Gil, James Cheney, Paul Groth, Olaf Hartig, Simon Miles, Luc Moreau, Paulo Pinherio da Silva. <a href='http://www.w3.org/2005/Incubator/prov/XGR-prov-20101214/'> Provenance XG Final Report.</a> December 2010.<a href='http://www.w3.org/2005/Incubator/prov/XGR-prov-20101214/'>http://www.w3.org/2005/Incubator/prov/XGR-prov-20101214/</a>",
};
var respecConfig = {
// specification status (e.g. WD, LCWD, NOTE, etc.). If in doubt use ED.
- specStatus: "WD-NOTE",
+ specStatus: "WG-NOTE",
// the specification's short name, as in http://www.w3.org/TR/short-name/
shortName: "prov-overview",
@@ -314,7 +314,7 @@
// if you wish the publication date to be other than today, set this
- publishDate: "2013-03-12",
+ publishDate: "2013-04-30",
// if the specification's copyright date is a range of years, specify
// the start date here:
@@ -322,7 +322,7 @@
// if there is a previously published draft, uncomment this and set its YYYY-MM-DD date
// and its maturity status
- previousPublishDate: "2012-12-11",
+ previousPublishDate: "2014-03-12",
previousMaturity: "WD",
// if there a publicly available Editor's Draft, this is the link
@@ -380,41 +380,53 @@
<section id="abstract">
<p>
Provenance is information about entities, activities, and people involved in producing a piece of data or thing, which can be used
-to form assessments about its quality, reliability or trustworthiness. The PROV Family of Documents defines a model, corresponding serializations and other supporting defintions to enable the inter-operable interchange of provenance information in heterogeneous environments such as the Web. This document provides an overview this family of documents.
+to form assessments about its quality, reliability or trustworthiness. The PROV Family of Documents defines a model, corresponding serializations and other supporting definitions to enable the inter-operable interchange of provenance information in heterogeneous environments such as the Web. This document provides an overview of this family of documents.
</section>
<section id="sotd">
-
<h4>PROV Family of Documents</h4>
This document is part of the PROV family of documents, a set of documents defining various aspects that are necessary to achieve the vision of inter-operable
-interchange of provenance information in heterogeneous environments such as the Web. These documents are listed below.
+interchange of provenance information in heterogeneous environments such as the Web. These documents are listed below.
+
<ul>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/">PROV-OVERVIEW</a> (To be published as Note), an overview of the PROV family of documents (this document);</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">PROV-PRIMER</a> (To be published as Note), a primer for the PROV data model [[PROV-PRIMER]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> (Proposed Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [[PROV-O]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> (Proposed Recommendation), the PROV data model for provenance; [[PROV-DM]]</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> (Proposed Recommendation), a notation for provenance aimed at human consumption [[PROV-N]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> (Proposed Recommendation), a set of constraints applying to the PROV data model [[PROV-CONSTRAINTS]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> (To be published as Note), an XML schema for the PROV data model [[PROV-XML]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">PROV-AQ</a> (To be published as Note), the mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">PROV-DICTIONARY</a> (To be published as Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> (To be published as Note) provides a mapping between PROV and Dublic Core Terms [[PROV-DC]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> (To be published as Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> (To be published as Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-overview-20130430/">PROV-OVERVIEW</a> (Note), an overview of the PROV family of documents (this document);</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-primer-20130430/">PROV-PRIMER</a> (Note), a primer for the PROV data model [[PROV-PRIMER]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-o-20130430/">PROV-O</a> (Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of the PROV data model to RDF [[PROV-O]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/">PROV-DM</a> (Recommendation), the PROV data model for provenance [[PROV-DM]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-n-20130430/">PROV-N</a> (Recommendation), a notation for provenance aimed at human consumption [[PROV-N]];</li>
+<li> <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/">PROV-CONSTRAINTS</a> (Recommendation), a set of constraints applying to the PROV data model [[PROV-CONSTRAINTS]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [[PROV-DC]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles . [[PROV-LINKS]]</li>
</ul>
+<h4>Implementations Encouraged</h4>
+<p>
+The Provenance Working Group encourages implementation of the specifications overviewed in this document.
+Although work on this document by the Provenance Working Group is complete,
+errors may be recorded in the <a href="http://www.w3.org/2011/prov/errata.html">errata</a> or and these may be addressed in future revisions.
+</p>
+
+<h4>Please Send Comments</h4>
+
</section>
<section id="introduction">
<h2>Introduction</h2>
-This document provides a non-normative overview of the PROV Family of Documents and provides a roadmap to using these these documents.
-Provenance is information about entities, activities, and people involved in producing a piece of data or thing, which can be used
-to form assessments about its quality, reliability or trustworthiness. The goal of PROV is to enable the wide publication and interchange of provenance on the Web and other information systems. PROV enables one to represent and interchange provenance information using widely available formats such as RDF and XML. In addition, it provides definitions for accessing provenance information, validating it, and mapping to Dublin Core.
+This document provides a non-normative overview of the PROV Family of Documents and provides a roadmap to using them.
+<a href="http://www.w3.org/TR/2013/REC-prov-dm-20130430/#dfn-provenance">Provenance</a> is information about entities, activities, and people involved in producing a piece of data or thing, which can be used
+to form assessments about its quality, reliability or trustworthiness. The goal of PROV is to enable the wide publication and interchange of provenance on the Web and other information systems. PROV enables one to represent and interchange provenance information using widely available formats such as RDF and XML. In addition, it provides definitions for accessing provenance information, validating it, and mapping to Dublin Core. When referring to PROV, we are referring to the entire family of documents.
+<p>
+The design of PROV stems from the recommendations of the Provenance Incubator Group ([[PROV-XG]]) which performed an extensive information gathering process including use case cataloging, requirements elicitation and a literature survey. From this process, <a href="http://www.w3.org/2005/Incubator/prov/XGR-prov-20101214/#Broad_Recommendations">8 broad recommendations were defined</a>. <a href="http://www.w3.org/2001/sw/wiki/PROV-FAQ#How_does_PROV_address_the_recommendations_of_the_Provenance_Incubator_Group">PROV supports seven of the eight recommendations.</a> Recommendation #2 was out of scope for standardization of activity of the working group, but it is believed that it can be supported by PROV extensibility points.
+</p>
<p>
-Below is the organization of PROV. At its core is a conceptual data model, which defines a common vocabulary used to describe provenance. This is instantiated by various serializations. These serializations are what are used by implementations to interchange provenance. To help developers and users create valid provenance, a set of constraints are defined, which can be used to create provenance validators. Finally, to further support the interchange of provenance, additional definitions are provided for protocols to locate and access provenance, connect sets of provenance descriptions and define how to interoperate with the widely used Dublin Core vocabulary.
+Below is the organization of PROV. At its core is a conceptual data model, which defines a common vocabulary used to describe provenance. This is instantiated by various serializations. These serializations are used by implementations to interchange provenance. To help developers and users express valid provenance, a set of constraints are defined, which can be used to implement provenance validators. Finally, to further support the interchange of provenance, additional specifications are provided for protocols to locate and access provenance, connect sets of provenance descriptions, and define how to interoperate with the widely used Dublin Core vocabulary.
</p>
<div>
@@ -425,37 +437,43 @@
<section id="roadmap">
<h2>Document Roadmap</h2>
-PROV consists of 12 documents (including this one). In order to use PROV, one need not be familiar with all of these documents. Indeed, PROV was specifically designed so that users and developers may get started quickly with basic usage and then incrementally progress to more advanced usage scenarios To help navigate PROV, each document is broadly classified as being intended for a specific audience.
+PROV consists of 12 documents (including this one). In order to use PROV, one need not be familiar with all of these documents. Indeed, PROV was specifically designed so that users and developers may get started quickly with basic usage and then incrementally progress to more advanced usage scenarios. To help navigate PROV, each document is broadly classified as being intended for a specific audience.
<ol>
<li> Users - this audience wants to understand PROV and use applications that support PROV.
<li> Developers - this audience wants to develop or build applications that create and consume provenance using PROV.
-<li> Advanced - this audience aims to create validators, new PROV serializations, or other advanced provenance systems.
+<li> Advanced - this audience aims to create validators, new PROV serializations, or other advanced provenance-based systems.
</ol>
-In the table below, we also denote the track that each document on whether it is intended to be a W3C Recommendation or a Working Group Note.
+In the table below, we also denote whether the document is a <a href="http://www.w3.org/2005/10/Process-20051014/tr#RecsW3C">W3C Recommendation</a> or a <a href="http://www.w3.org/2005/10/Process-20051014/tr#WGNote">Working Group Note.</a>
<table class="open-data-table">
<tr><th>Part</th><th>Audience</th><th>Type</th><th>Document</th></tr>
-<tr><td style="text-align: center;">1</td><td style="background: #DFF">Users</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">PROV-PRIMER</a> is the entry point to PROV offering an introduction to the provenance model. This is where you should start and for many may be the only document needed.</td></tr>
-<tr><td style="text-align: center;">2</td><td style="background: #CDD">Developers</td><td>Rec</td><td><a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> defines a light-weight OWL2 ontology for the provenance model. This is intended for the Linked Data and Semantic Web community. </td></tr>
-<tr><td style="text-align: center;">3</td><td style="background: #CDD">Developers</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> defines an XML schema for the provenance model. This is intended for developers who need a native XML serialization of PROV</td></tr>
-<tr><td style = "text-align: center;">4</td><td style="background: #FDD">Advanced</td><td>Rec</td><td><a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> defines a conceptual data model for provenance including UML diagrams. PROV-O and PROV-XML are serializations of this conceptual model.</td></tr>
-<tr><td style = "text-align: center;">5</td><td style="background: #FDD">Advanced</td><td>Rec</td><td><a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> defines a human-readable notation for provenance. This is used to define the conceptual model as well as PROV-CONSTRAINTS. </td></tr>
-<tr><td style = "text-align: center;">6</td> <td style="background: #FDD">Advanced</td><td>Rec</td><td> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> defines a set constraints that define a notion of valid provenance. It is specifically aimed at the implementors of validators. </td></tr>
+<tr><td style="text-align: center;">1</td><td style="background: #DFF">Users</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">PROV-PRIMER</a> is the entry point to PROV offering an introduction to the provenance data model. This is where you should start and for many may be the only document needed.</td></tr>
+<tr><td style="text-align: center;">2</td><td style="background: #CDD">Developers</td><td>Rec</td><td><a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> defines a light-weight OWL2 ontology for the provenance data model. This is intended for the Linked Data and Semantic Web community. </td></tr>
+<tr><td style="text-align: center;">3</td><td style="background: #CDD">Developers</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> defines an XML schema for the provenance data model. This is intended for developers who need a native XML serialization of the PROV data model.</td></tr>
+<tr><td style = "text-align: center;">4</td><td style="background: #FDD">Advanced</td><td>Rec</td><td><a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> defines a conceptual data model for provenance including UML diagrams. PROV-O, PROV-XML and PROV-N are serializations of this conceptual model.</td></tr>
+<tr><td style = "text-align: center;">5</td><td style="background: #FDD">Advanced</td><td>Rec</td><td><a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> defines a human-readable notation for the provenance model. This is used to provide examples within the conceptual model as well as used in the definition of PROV-CONSTRAINTS. </td></tr>
+<tr><td style = "text-align: center;">6</td> <td style="background: #FDD">Advanced</td><td>Rec</td><td> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> defines a set of constraints on the PROV data model that specifies a notion of valid provenance. It is specifically aimed at the implementors of validators. </td></tr>
<tr><td style="text-align: center;">7</td><td style="background: #CDD">Developers</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">PROV-AQ</a> defines how to use Web-based mechanisms to locate and retrieve provenance information. </td></tr>
-<tr><td style="text-align: center;">8</td><td style="background: #CDD">Developers</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> defines a mapping between Dublin Core and PROV. </td></tr>
+<tr><td style="text-align: center;">8</td><td style="background: #CDD">Developers</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> defines a mapping between Dublin Core and PROV-O. </td></tr>
<tr><td style="text-align: center;">9</td><td style="background: #CDD">Developers</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DICTIONARY</a> defines constructs for expressing the provenance of dictionary style data structures. </td></tr>
-<tr><td style="text-align: center;">10</td><td style="background: #FDD">Advanced</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> defines a declarative specification in terms of first-order logic of the PROV data model;</li></td></tr>
-<tr><td style = "text-align: center;">11</td><td style="background: #FDD">Advanced</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> Defines extensions to PROV to enable linking provenance information across containers for provenance</td></tr>
+<tr><td style="text-align: center;">10</td><td style="background: #FDD">Advanced</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> defines a declarative specification in terms of first-order logic of the PROV data model.</li></td></tr>
+<tr><td style = "text-align: center;">11</td><td style="background: #FDD">Advanced</td><td>Note</td><td><a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> defines extensions to PROV to enable linking provenance information across bundles of provenance description.</td></tr>
</table>
</section>
<section>
+<h2>Namespace</h2>
+All terms defined within PROV are defined within the namespace <a href="http://www.w3.org/ns/prov#">http://www.http://www.w3.org/ns/prov#</a>. The prefix convention that is used is <b>prov</b>. Thus, no matter which document you use the namespace will be the same. The decision was made to simplify the usage of PROV.
+</section>
+
+
+<section>
<h2>Additional Information</h2>
-In addition, to these specifications, the <a href="http://www.w3.org/2001/sw/wiki/PROV-FAQ">PROV FAQ</a> page addresses common questions as well as sets PROV in a broader context. This page is continually updated. Working group members have also given several <a href="http://www.w3.org/2011/prov/wiki/OutreachInformation">tutorials</a> about PROV including hands-on exercises, these may be a useful place to start. In addition, one can find a variety of blog posts and web pages on PROV - a short list can be found <a href="http://www.w3.org/2011/prov/wiki/OutreachInformation">here</a>.
+In addition, to these specifications, the <a href="http://www.w3.org/2001/sw/wiki/PROV-FAQ">PROV FAQ</a> page addresses common questions as well as sets PROV in a broader context. This page is continually updated. Working group members have also given several <a href="http://www.w3.org/2001/sw/wiki/PROV-Outreach">tutorials</a> about PROV including hands-on exercises, these may be a useful place to start. In addition, one can find a variety of blog posts and web pages on PROV - a short list can be found <a href="http://www.w3.org/2001/sw/wiki/PROV-Outreach">here</a>.
For a broader review of provenance that led to the creation of PROV, there are several reports produced by the <a href="http://www.w3.org/2005/Incubator/prov/wiki/W3C_Provenance_Incubator_Group_Wiki">W3C Provenance Incubator group</a> including:
@@ -465,6 +483,7 @@
<li> <a href="http://www.w3.org/2005/Incubator/prov/XGR-prov-20101214/#State_of_the_art_and_technology_gaps">State of the Art Report</a></li>
</ol>
+
Finally, the simplest way to use PROV is through one of the many applications that support it. Please see the group's <a href="http://www.w3.org/TR/2013/WD-prov-implementations-20130312/">implementation report</a> that highlights reported implementations of PROV.
@@ -481,7 +500,21 @@
-<section class="appendix">
+<section class="appendix">
+<h2>Change Log</h2>
+<section>
+ <h3>Change Log Since WD Working Draft 12 March 2013</h3>
+<ul>
+<li> Changed the status of this document section.
+<li> Changed all URLs to PROV documents.
+<li> Updated the figure to move prov-n outside of prov-dm and to put prov-dc on top of prov-o.
+<li> Added section on namespaces.
+<li> Added a paragraph discussing the broad recommendations from the incubator group.
+<li> Editorial pass following reviews.
+</ul>
+</section>
+
+<section>
<h2>Acknowledgements</h2>
<p>
--- a/paq/css/prov-aq.css Sun Apr 14 19:43:18 2013 +0200
+++ b/paq/css/prov-aq.css Sun Apr 14 19:44:18 2013 +0200
@@ -10,6 +10,11 @@
color: #224433;
}
+td code {
+ font-family: monospace;
+ color: #224433;
+}
+
div code {
font-family: monospace;
color: #224433;
--- a/paq/prov-aq.html Sun Apr 14 19:43:18 2013 +0200
+++ b/paq/prov-aq.html Sun Apr 14 19:44:18 2013 +0200
@@ -387,9 +387,6 @@
<section>
<h2>URI types and dereferencing</h2>
- <p class="TODO">
- Proposed to drop Target-URI entry from this section.
- </p>
<p>
A number of resource types are described above in <a href="#concepts" class="sectionRef"></a>. The table below summarizes what these various URIs are intended to denote, and the kind of information that should be returned if they are dereferenced:
</p>
@@ -402,7 +399,10 @@
<tr style="vertical-align: top;">
<td><a class="internalDFN">Target-URI</a></td>
<td>Any resource that is described by some provenance - typically an <a class="externalRef" href="http://www.w3.org/TR/prov-dm/#section-entity-activity">entity</a> (in the sense of [[PROV-DM]]), but may be of another type (such as [[PROV-DM]] activity).</td>
- <td>If the URI is dereferencable, it should return a representation or description of the resource for which provenance is provided.</td>
+ <td>
+ Not specified (the URI is not even required to be dereferencable).
+ <!-- If the URI is dereferencable, it should return a representation or description of the resource for which provenance is provided. -->
+ </td>
</tr>
<tr style="vertical-align: top;">
<td><a class="internalDFN">Provenance-URI</a></td>
@@ -966,9 +966,6 @@
<section>
<h2>Provenance pingback</h2>
- <p class="TODO">
- REVIEW. This section describes an "at-risk" feature whose final inclusion in this document is undecided. Does the use of a "ping-back" for discovering additional provenance fall under the remit of "provenance access and query"? Is it a useful feature to define?
- </p>
<p>
This section describes a mechanism that may be used to discover related provenance information that the publisher of a resource does not otherwise know about; e.g. provenance describing how it is used after it has been created.
</p>
@@ -1001,20 +998,20 @@
For example, consider a resource that is published by <code>acme.example.com</code>, and is subsequently used by <code>coyote.example.org</code> in the construction of some new entity; we might see an exchange along the following lines. We start with <code>coyote.example.org</code> retrieving a copy of <code>acme.example.org</code>'s resource:
</p>
<pre class="example code">
- C: GET http://acme.example.org/super-widget HTTP/1.1
+ C: GET http://acme.example.org/super-widget123 HTTP/1.1
S: 200 OK
- S: Link: <http://acme.example.org/super-widget/provenance>;
+ S: Link: <http://acme.example.org/super-widget123/provenance>;
rel="http://www.w3.org/ns/prov#has_provenance"
- S: Link: <http://acme.example.org/super-widget/pingback>;
+ S: Link: <http://acme.example.org/super-widget123/pingback>;
rel="http://www.w3.org/ns/prov#pingback"
:
- (super-widget resource data)</pre>
+ (super-widget123 resource data)</pre>
<p>
- The first of the links in the response is a <code>has_provenance</code> link with a <a class="internalDFN">provenance-URI</a> that has been described previously (<a href="#resource-accessed-by-http" class="sectionRef"></a>). The second is a distinct resource that exists to receive provenance pingbacks. Later, when a new resource has been created or some related action performed based upon the <code>acme.example.org/super-widget</code>, a client may post a pingback request to any supplied <code>pingback</code> URI:
+ The first of the links in the response is a <code>has_provenance</code> link with a <a class="internalDFN">provenance-URI</a> that has been described previously (<a href="#resource-accessed-by-http" class="sectionRef"></a>). The second is a distinct resource that exists to receive provenance pingbacks. Later, when a new resource has been created or some related action performed based upon the <code>acme.example.org/super-widget123</code>, a client may post a pingback request to the supplied <code>pingback</code> URI:
</p>
<pre class="example code">
- C: POST http://acme.example.org/super-widget/pingback HTTP/1.1
+ C: POST http://acme.example.org/super-widget123/pingback HTTP/1.1
C: Content-Type: text/uri-list
C:
C: http://coyote.example.org/contraption/provenance
@@ -1033,10 +1030,10 @@
The only defined operation on a pingback-URI is POST, which supplies links to provenance information or services as described above. A pingback-URI MAY respond to other requests, but no requirements are imposed on how it responds. In particular, it is not specified here how a pingback resource should respond to an HTTP GET request.
</p>
<p>
- The pingback client MAY include extra <code>has_provenance</code> links to indicate provenance records related to a different resources, specified with correspondingly different anchor URIs. For example:
+ The pingback client MAY include extra <code>has_provenance</code> links to indicate provenance records related to a different resources, specified with correspondingly different anchor URIs. These MAY indicate further provenance about existing resources, or about new resources (such as new entities derived or specialized from that for which the pingback URI was provided). For example:
</p>
<pre class="example code">
- C: POST http://acme.example.org/super-widget/pingback HTTP/1.1
+ C: POST http://acme.example.org/super-widget123/pingback HTTP/1.1
C: Link: <http://coyote.example.org/extra/provenance>;
rel="http://www.w3.org/ns/prov#has_provenance";
anchor="http://acme.example.org/extra-widget"
@@ -1049,13 +1046,13 @@
S: 204 No Content
</pre>
<p>
- The client MAY also supply <code>has_query_service</code> links indicating provenance query services that can describe the target-URI. The anchor MUST be included, and SHOULD be either the target-URI of the resource for which the pingback URI was provided (from the examples above, that would be <code>http://acme.example.org/super-widget</code>), or some related resource with relevant provenance. For example:
+ The client MAY also supply <code>has_query_service</code> links indicating provenance query services that can describe the target-URI. The anchor MUST be included, and SHOULD be either the target-URI of the resource for which the pingback URI was provided (from the examples above, that would be <code>http://acme.example.org/super-widget123</code>), or some related resource with relevant provenance. For example:
</p>
<pre class="example code">
- C: POST http://acme.example.org/super-widget/pingback HTTP/1.1
+ C: POST http://acme.example.org/super-widget123/pingback HTTP/1.1
C: Link: <http://coyote.example.org/sparql>;
rel="http://www.w3.org/ns/prov#has_query_service";
- anchor="http://acme.example.org/super-widget"
+ anchor="http://acme.example.org/super-widget123"
C: Content-Type: text/uri-list
C: Content-Length: 0
C:
@@ -1063,7 +1060,7 @@
S: 204 No Content
</pre>
<p>
- Here, the pingback client has supplied a query service URI, but did not submit any provenance-URIs and the URI list is therefore empty. The <code>Link</code> header field indicates that the resource <code>http://acme.example.org/super-widget/provenance</code> contains provenance information relating to <code>http://acme.example.org/super-widget</code> (that being the URI of the resource for which the pingback URI was provided).
+ Here, the pingback client has supplied a query service URI, but did not submit any provenance-URIs and the URI list is therefore empty. The <code>Link</code> header field indicates that the resource <code>http://acme.example.org/super-widget123/provenance</code> contains provenance information relating to <code>http://acme.example.org/super-widget123</code> (that being the URI of the resource for which the pingback URI was provided).
</p>
<!-- also in Stian's proposal
@@ -1268,6 +1265,10 @@
prov-aq.html
-->
<dl>
+<dt>2013-04-12 12:07 +0100 dae5268c75c0 Graham Klyne</dt><dd>Add some text clarifying that pingback provenance may be about new entities; result of dereferencing 'target-URI' not specified</dd>
+<dt>2013-04-12 11:32 +0100 a89cc91fa022 Graham Klyne</dt><dd>Remove 'at risk' note from section on pingback</dd>
+<dt>2013-04-12 11:31 +0100 318ae02bca82 Graham Klyne</dt><dd>Change example URIs in pingback description to make it clearer they are instances (e.g. http://acme.example.org/super-widget123)</dd>
+<dt>2013-04-08 10:33 +0100 3ddca8678084 Graham Klyne</dt><dd>Update change log</dd>
<dt>2013-04-08 10:30 +0100 2de1db892bfc Graham Klyne</dt><dd>Various editorial fixes; drop note about possibility of service document description from LDP WG.</dd>
<dt>2013-04-05 18:20 +0100 8b6a3e6e27c8 Graham Klyne</dt><dd>Additions and TODO in acknowledgements section.</dd>
<dt>2013-04-05 18:15 +0100 2072b00f4563 Graham Klyne</dt><dd>Fix typo</dd>
--- a/primer/NOTE-prov-primer-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/primer/NOTE-prov-primer-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -242,7 +242,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
- <li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+ <li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
@@ -2238,7 +2238,7 @@
</section>
-<section id="references" class="appendix"><!--OddPage--><h2><span class="secno">C. </span>References</h2><section id="informative-references"><h3><span class="secno">C.1 </span>Informative references</h3><dl class="bibliography"><dt id="bib-DCTERMS">[DCTERMS]</dt><dd>Dublin Core Metadata Initiative. <a href="http://dublincore.org/documents/2012/06/14/dcmi-terms/"><cite>Dublin Core Terms Vocabulary</cite></a>. 14 June 2012. URL: <a href="http://dublincore.org/documents/2012/06/14/dcmi-terms/">http://dublincore.org/documents/2012/06/14/dcmi-terms/</a>
+<section id="references" class="appendix"><!--OddPage--><h2><span class="secno">C. </span>References</h2><section id="informative-references"><h3><span class="secno">C.1 </span>Informative references</h3><dl class="bibliography"><dt id="bib-DCTERMS">[DCTERMS]</dt><dd>Dublin Core Metadata Initiative. <a href="http://dublincore.org/documents/2012/06/14/dcmi-terms/"><cite>DCMI Metadata Terms</cite></a>. 14 June 2012. URL: <a href="http://dublincore.org/documents/2012/06/14/dcmi-terms/">http://dublincore.org/documents/2012/06/14/dcmi-terms/</a>
</dd><dt id="bib-FOAF">[FOAF]</dt><dd>Dan Brickley, Libby Miller; eds. <a href="http://xmlns.com/foaf/spec/20100809.html"><cite>FOAF Vocabulary Specification 0.98</cite></a>. 9 August 2010. URL: <a href="http://xmlns.com/foaf/spec/20100809.html">http://xmlns.com/foaf/spec/20100809.html</a>
</dd><dt id="bib-PROV-AQ">[PROV-AQ]</dt><dd>Graham Klyne; Paul Groth; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/"><cite>Provenance Access and Query</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/</a>
</dd><dt id="bib-PROV-CONSTRAINTS">[PROV-CONSTRAINTS]</dt><dd>James Cheney; Paolo Missier; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/"><cite>Constraints of the PROV Data Model</cite></a>. 30 April 2013, W3C Recommendation. URL: <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/">http://www.w3.org/TR/2013/REC-prov-constraints-20130430/</a>
--- a/primer/Primer.html Sun Apr 14 19:43:18 2013 +0200
+++ b/primer/Primer.html Sun Apr 14 19:44:18 2013 +0200
@@ -42,7 +42,7 @@
"URL: <a href=\"http://xmlns.com/foaf/spec/20100809.html\">http://xmlns.com/foaf/spec/20100809.html</a>",
"DCTERMS":
"Dublin Core Metadata Initiative. " +
- "<a href=\"http://dublincore.org/documents/2012/06/14/dcmi-terms/\"><cite>Dublin Core Terms Vocabulary</cite></a>. " +
+ "<a href=\"http://dublincore.org/documents/2012/06/14/dcmi-terms/\"><cite>DCMI Metadata Terms</cite></a>. " +
"14 June 2012. " +
"URL: <a href=\"http://dublincore.org/documents/2012/06/14/dcmi-terms/\">http://dublincore.org/documents/2012/06/14/dcmi-terms/</a>"
};
@@ -154,7 +154,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
- <li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublic Core Terms [[PROV-DC]];</li>
+ <li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV-O and Dublin Core Terms [[PROV-DC]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a> (Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
</ul>
--- a/provenance/prov-dm.ttl Sun Apr 14 19:43:18 2013 +0200
+++ b/provenance/prov-dm.ttl Sun Apr 14 19:44:18 2013 +0200
@@ -2,6 +2,6 @@
@prefix prov: <http://www.w3.org/ns/prov#> .
-<http://www.w3.org/TR/prov-dm/> a prov:Entity.
+<http://www.w3.org/TR/prov-dm> a prov:Entity.
--- a/reports/NOTE-prov-implementations-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/reports/NOTE-prov-implementations-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -17,7 +17,7 @@
color: #b9ab2d;
}
div.issue-title { color: #e05252; }
-div.note-title { color: #52e052; }
+div.note-title { color: #2b2; }
div.issue-title span, div.note-title span {
text-transform: uppercase;
}
@@ -32,7 +32,7 @@
border-left-style: solid;
}
div.issue, div.note {
- padding: 0.5em;
+ padding: 1em 1.2em 0.5em;
margin: 1em 0;
position: relative;
clear: both;
@@ -183,9 +183,6 @@
<dd><a href="http://www.w3.org/TR/prov-implementations/">http://www.w3.org/TR/prov-implementations/</a></dd>
- <dt>Latest editor's draft:</dt>
- <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/reports/prov-implementations.html">http://dvcs.w3.org/hg/prov/raw-file/default/reports/prov-implementations.html</a></dd>
-
@@ -236,9 +233,8 @@
index</a> at http://www.w3.org/TR/.</em>
</p>
- During the Candidate Recommendation period of PROV, implementation experience was reported. This document summarises those experiences. The version at <a href="http://www.w3.org/TR/2013/WD-prov-implementations-20130312/">http://www.w3.org/TR/2013/WD-prov-implementations-20130312/</a> is the version used for purposes of transition to proposed recommendation.
-
-For comments, please send a mail to <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a> [<a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archive</a>].
+ During the lifetime of the Provenance Working Group, implementation experience of the PROV specifications was reported. This document summarises those experiences. The version at <a href="http://www.w3.org/TR/2013/WD-prov-implementations-20130312/">http://www.w3.org/TR/2013/WD-prov-implementations-20130312/</a> is the version used for purposes of transition to proposed recommendation.
+ For comments, please send a mail to <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a> [<a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archive</a>].
<p>
This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as a Working Group Note.
@@ -285,7 +281,7 @@
</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#Introduction" class="tocxref"><span class="secno">1. </span>Introduction</a><ul class="toc"><li class="tocline"><a href="#Exit-Criteria" class="tocxref"><span class="secno">1.1 </span> Meeting the Exit Criteria</a></li></ul></li><li class="tocline"><a href="#implementations" class="tocxref"><span class="secno">2. </span>List of Implementations</a></li><li class="tocline"><a href="#Feature-Coverage" class="tocxref"><span class="secno">3. </span> Feature Coverage</a><ul class="toc"><li class="tocline"><a href="#prov-terms" class="tocxref"><span class="secno">3.1 </span>PROV Usage </a></li><li class="tocline"><a href="#prov-extensions" class="tocxref"><span class="secno">3.2 </span>PROV Usage by Extension</a></li><li class="tocline"><a href="#prov-usage" class="tocxref"><span class="secno">3.3 </span>PROV Usage in Datasets</a></li><li class="tocline"><a href="#prov-contraints" class="tocxref"><span class="secno">3.4 </span>PROV Constraints Implementation</a></li></ul></li><li class="tocline"><a href="#prov-exchange" class="tocxref"><span class="secno">4. </span>Implementations Exchanging Provenance</a></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">A. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">B. </span>References</a><ul class="toc"><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">B.1 </span>Informative references</a></li></ul></li></ul></section>
-
+
<section id="Introduction">
<!--OddPage--><h2><span class="secno">1. </span>Introduction</h2>
@@ -309,7 +305,7 @@
<section id="Exit-Criteria">
<h3><span class="secno">1.1 </span> Meeting the Exit Criteria</h3>
- <p>At the start of the Candidate Recommendation phase, the Working Group defined <a href="http://www.w3.org/2011/prov/wiki/ProvCRExitCriteria">a series of exit criteria</a>. These exit criteria can be summarized as for each feature defined by PROV there are at least two implementations that support the feature and that there exists one interoperability pair that can exchange that feature. Section <a href="#prov-terms">3.1</a> shows that a minimum of 4 implementations both produce and consume all constructs defined in PROV-DM. PROV-O is implemented by over 40 implementations and PROV-N is implemented by 7 implementations.</p>
+ <p>At the start of the Candidate Recommendation phase, the Working Group defined <a href="http://www.w3.org/2011/prov/wiki/ProvCRExitCriteria">a series of exit criteria</a>. These exit criteria can be summarized as for each feature defined by PROV there are at least two implementations that support the feature and that there exists one interoperability pair that can exchange that feature. Section <a href="#prov-terms">3.1</a> shows that three implementations both produce and consume all constructs defined in PROV-DM. PROV-O is implemented by over 40 implementations and PROV-N is implemented by 12 implementations.</p>
<p>In terms of implementation pairs, Section <a href="#prov-exchange">4</a> enumerates which pairs of implementations report exchanging provenance. Here, we meet the exit criteria in that each feature is exchanged by at least two implementations.</p>
<p>Finally, three validators have implemented all of the constraints defined in PROV-Constraints passing the requisite test cases, thus, passing the exit criteria. The working group recognizes that implementing the PROV-Constraints document requires substantial effort. It is nice to see that three radically different approaches were chosen to implement this specification: SPARQL, Java, Prolog, which speaks to the implementability of this specification.</p>
<p>For a systematic enumeration of how the exit criteria were met, please see <a href="http://www.w3.org/2011/prov/wiki/MeetingProvCRExitCriteria"> http://www.w3.org/2011/prov/wiki/MeetingProvCRExitCriteria</a></p>
@@ -362,7 +358,7 @@
</tr>
<tr id="5">
<td>5</td>
- <th scope="row"><a href="http://www.collabmap.org/">CollabMap</a></th>
+ <th scope="row"><a href="http://www.orchid.ac.uk/collabmap">CollabMap</a></th>
<td>Application</td>
<td>PROV-JSON</td>
</tr>
@@ -376,7 +372,7 @@
<td>7</td>
<th scope="row"><a href="https://github.com/lucmoreau/ProvToolbox">ProvToolbox</a></th>
<td>Framework / API<br>Service</td>
- <td>PROV-O, PROV-N, PROV-XML, prov-json</td>
+ <td>PROV-O, PROV-N, PROV-XML, PROV-JSON</td>
</tr>
<tr id="8">
<td>8</td>
@@ -434,13 +430,13 @@
</tr>
<tr id="17">
<td>17</td>
- <th scope="row"><a href="https://provenance.ecs.soton.ac.uk/store">Provenance server</a></th>
+ <th scope="row"><a href="https://provenance.ecs.soton.ac.uk/store/">Provenance server</a></th>
<td>Service</td>
<td>PROV-N, PROV-JSON</td>
</tr>
<tr id="18">
<td>18</td>
- <th scope="row"><a href="http://hac.ecs.soton.ac.uk/agentswitch/">agentSwitch</a></th>
+ <th scope="row"><a href="http://www.orchid.ac.uk/agentswitch">agentSwitch</a></th>
<td>Application</td>
<td>PROV-N, PROV-JSON</td>
</tr>
@@ -620,7 +616,7 @@
</tr>
<tr id="48">
<td>48</td>
- <th scope="row"><a href="http://purl.org/net/provenance/ns">Jun Zhao</a></th>
+ <th scope="row"><a href="http://purl.org/net/provenance/ns">Provenance Vocabulary Core Ontology Specification</a></th>
<td>Vocabulary Extension</td>
<td>PROV-O</td>
</tr>
@@ -722,7 +718,7 @@
</tr>
<tr id="65">
<td>65</td>
- <th scope="row"><a href="http://provenance.ecs.soton.ac.uk/validator/validator.html">ProvValidator</a></th>
+ <th scope="row"><a href="http://provenance.ecs.soton.ac.uk/validator/validator.html">Prov-Validator</a></th>
<td>Validator</td>
<td>PROV-O, PROV-N, PROV-XML, PROV-JSON</td>
</tr>
@@ -2452,7 +2448,7 @@
<th scope="col"><a href="#45" title="roevo">#45</a></th>
<th scope="col"><a href="#46" title="wfprov">#46</a></th>
<th scope="col"><a href="#47" title="P-plan">#47</a></th>
- <th scope="col"><a href="#48" title="Jun Zhao">#48</a></th>
+ <th scope="col"><a href="#48" title="Provenance Vocabulary Core Ontology Specification">#48</a></th>
<th scope="col"><a href="#49" title="Systems molecular biology provenance ontology (SysPro) ">#49</a></th>
<th scope="col"><a href="#50" title="Yanfeng Shu">#50</a></th>
<th scope="col"><a href="#51" title="ISO_19115_Lineage">#51</a></th>
@@ -3527,9 +3523,9 @@
</caption>
<tbody><tr>
<th scope="col">Constraint</th>
- <th scope="col"> <a href="#64" title="prov-check">#62</a></th>
- <th scope="col"><a href="#65" title="checker.pl">#63</a></th>
- <th scope="col"><a href="#66" title="ProvValidator">#64</a></th>
+ <th scope="col"> <a href="#64" title="prov-check">#64</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
+ <th scope="col"><a href="#66" title="checker.pl">#66</a></th>
</tr>
<tr>
<td class="feature"><a href="http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#key-object">Constraint 22 (key-object)</a></td>
@@ -3764,7 +3760,7 @@
<th scope="col">Provenenane Server</th>
<th scope="col">APROVeD</th>
<th scope="col">PROV Python</th>
- <th scope="col">ProvValidator</th>
+ <th scope="col">Prov-Validator</th>
<th scope="col">PROV-DM</th>
</tr>
<tr><td colspan="9"></td></tr>
@@ -3780,7 +3776,7 @@
<td> </td>
</tr>
<tr>
- <th scope="row"><a href="#65">ProvValidator</a></th>
+ <th scope="row"><a href="#65">Prov-Validator</a></th>
<td> </td>
<td><span class="independent-impl">All (PROV-O)</span></td>
<td><span class="independent-codebase">All (PROV-N)</span></td>
@@ -3803,8 +3799,8 @@
</tbody></table>
<p>Summary:</p>
<ul>
- <li>The Provenance Server (University of Southampton, Python code base) consumes provenance documents deposited by the ProvToolbox Converter and ProvValidator (University of Southampton, Java code base)</li>
- <li>The ProvValidator (University of Southampton) validates:
+ <li>The Provenance Server (University of Southampton, Python code base) consumes provenance documents deposited by the ProvToolbox Converter and Prov-Validator (University of Southampton, Java code base)</li>
+ <li>The Prov-Validator (University of Southampton) validates:
<ul>
<li>All PROV-O terms generated by PROVoKing (King's College London)</li>
<li>All PROV-N terms generated by the Provenance Server and the PROV-Python library (University of Southampton, Python code base)</li>
@@ -3831,11 +3827,11 @@
</tr>
<tr>
<th scope="col">Consumer:</th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
<th scope="col"><a href="#64" title="prov-check">#64</a></th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
</tr>
<tr>
<th scope="col">Term</th>
@@ -4190,7 +4186,7 @@
<td>2</td>
</tr>
</tbody></table>
- <div class="note"><div class="note-title"><span>Note</span></div><p class="">Although the Provenance Server (#17) and the ProvValidator (#65) are from the same institution (i.e. University of Southampton), it is worth noting that they were built from two independent code bases (one in Python and the other in Java)</p></div>
+ <div class="note"><div class="note-title"><span>Note</span></div><p class="">Although the Provenance Server (#17) and the Prov-Validator (#65) are from the same institution (i.e. University of Southampton), it is worth noting that they were built from two independent code bases (one in Python and the other in Java)</p></div>
</section>
<section class="appendix" id="acknowledgements">
--- a/reports/prov-implementations.html Sun Apr 14 19:43:18 2013 +0200
+++ b/reports/prov-implementations.html Sun Apr 14 19:44:18 2013 +0200
@@ -35,7 +35,7 @@
previousMaturity: "WD-NOTE",
// if there a publicly available Editor's Draft, this is the link
- edDraftURI: "http://dvcs.w3.org/hg/prov/raw-file/default/reports/prov-implementations.html",
+ // edDraftURI: "http://dvcs.w3.org/hg/prov/raw-file/default/reports/prov-implementations.html",
// if this is a LCWD, uncomment and set the end of its review period
// lcEnd: "2009-08-05",
@@ -49,9 +49,9 @@
editors: [
{ name: "Trung Dong Huynh", url: "http://www.ecs.soton.ac.uk/~tdh/",
company: "University of Southampton" },
- { name: "Paul Groth", url: "http://www.few.vu.nl/~pgroth/",
+ { name: "Paul Groth", url: "http://www.few.vu.nl/~pgroth/",
company: "VU University Amsterdam" },
- { name: "Stephan Zednik", url: "http://tw.rpi.edu/web/person/StephanZednik",
+ { name: "Stephan Zednik", url: "http://tw.rpi.edu/web/person/StephanZednik",
company: "Rensselaer Polytechnic Institute" },
],
@@ -87,10 +87,9 @@
<section id="abstract">
<p>This document reports on implementations and usage of the four normative specifications ([[PROV-DM]], [[PROV-N]], [[PROV-O]], [[PROV-CONSTRAINTS]]) of the PROV Family of Documents [[PROV-OVERVIEW]]. In particular, it's aim is to demonstrate that the features defined in PROV are implementable and interoperable. Features are defined as: the constructs specified in [[PROV-DM]] and their realisation in OWL (see [[PROV-O]]) and in the [[PROV-N]] syntax; the constraints defined within [[PROV-CONSTRAINTS]]. Interoperability is defined through both the interchange of provenance information and the coverage of test cases. </p>
</section>
- <section id="sotd">
- During the Candidate Recommendation period of PROV, implementation experience was reported. This document summarises those experiences. The version at <a href="http://www.w3.org/TR/2013/WD-prov-implementations-20130312/">http://www.w3.org/TR/2013/WD-prov-implementations-20130312/</a> is the version used for purposes of transition to proposed recommendation.
-
-For comments, please send a mail to <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a> [<a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archive</a>].
+ <section id="sotd">
+ During the lifetime of the Provenance Working Group, implementation experience of the PROV specifications was reported. This document summarises those experiences. The version at <a href="http://www.w3.org/TR/2013/WD-prov-implementations-20130312/">http://www.w3.org/TR/2013/WD-prov-implementations-20130312/</a> is the version used for purposes of transition to proposed recommendation.
+ For comments, please send a mail to <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a> [<a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archive</a>].
</section>
<section id="Introduction">
@@ -115,7 +114,7 @@
<section id="Exit-Criteria">
<h2> Meeting the Exit Criteria</h2>
- <p>At the start of the Candidate Recommendation phase, the Working Group defined <a href="http://www.w3.org/2011/prov/wiki/ProvCRExitCriteria">a series of exit criteria</a>. These exit criteria can be summarized as for each feature defined by PROV there are at least two implementations that support the feature and that there exists one interoperability pair that can exchange that feature. Section <a href="#prov-terms">3.1</a> shows that a minimum of 4 implementations both produce and consume all constructs defined in PROV-DM. PROV-O is implemented by over 40 implementations and PROV-N is implemented by 7 implementations.</p>
+ <p>At the start of the Candidate Recommendation phase, the Working Group defined <a href="http://www.w3.org/2011/prov/wiki/ProvCRExitCriteria">a series of exit criteria</a>. These exit criteria can be summarized as for each feature defined by PROV there are at least two implementations that support the feature and that there exists one interoperability pair that can exchange that feature. Section <a href="#prov-terms">3.1</a> shows that three implementations both produce and consume all constructs defined in PROV-DM. PROV-O is implemented by over 40 implementations and PROV-N is implemented by 12 implementations.</p>
<p>In terms of implementation pairs, Section <a href="#prov-exchange">4</a> enumerates which pairs of implementations report exchanging provenance. Here, we meet the exit criteria in that each feature is exchanged by at least two implementations.</p>
<p>Finally, three validators have implemented all of the constraints defined in PROV-Constraints passing the requisite test cases, thus, passing the exit criteria. The working group recognizes that implementing the PROV-Constraints document requires substantial effort. It is nice to see that three radically different approaches were chosen to implement this specification: SPARQL, Java, Prolog, which speaks to the implementability of this specification.</p>
<p>For a systematic enumeration of how the exit criteria were met, please see <a href="http://www.w3.org/2011/prov/wiki/MeetingProvCRExitCriteria"> http://www.w3.org/2011/prov/wiki/MeetingProvCRExitCriteria</a></p>
@@ -168,7 +167,7 @@
</tr>
<tr id="5">
<td>5</td>
- <th scope="row"><a href="http://www.collabmap.org/">CollabMap</a></th>
+ <th scope="row"><a href="http://www.orchid.ac.uk/collabmap">CollabMap</a></th>
<td>Application</td>
<td>PROV-JSON</td>
</tr>
@@ -182,7 +181,7 @@
<td>7</td>
<th scope="row"><a href="https://github.com/lucmoreau/ProvToolbox">ProvToolbox</a></th>
<td>Framework / API<br>Service</td>
- <td>PROV-O, PROV-N, PROV-XML, prov-json</td>
+ <td>PROV-O, PROV-N, PROV-XML, PROV-JSON</td>
</tr>
<tr id="8">
<td>8</td>
@@ -240,13 +239,13 @@
</tr>
<tr id="17">
<td>17</td>
- <th scope="row"><a href="https://provenance.ecs.soton.ac.uk/store">Provenance server</a></th>
+ <th scope="row"><a href="https://provenance.ecs.soton.ac.uk/store/">Provenance server</a></th>
<td>Service</td>
<td>PROV-N, PROV-JSON</td>
</tr>
<tr id="18">
<td>18</td>
- <th scope="row"><a href="http://hac.ecs.soton.ac.uk/agentswitch/">agentSwitch</a></th>
+ <th scope="row"><a href="http://www.orchid.ac.uk/agentswitch">agentSwitch</a></th>
<td>Application</td>
<td>PROV-N, PROV-JSON</td>
</tr>
@@ -426,7 +425,7 @@
</tr>
<tr id="48">
<td>48</td>
- <th scope="row"><a href="http://purl.org/net/provenance/ns">Jun Zhao</a></th>
+ <th scope="row"><a href="http://purl.org/net/provenance/ns">Provenance Vocabulary Core Ontology Specification</a></th>
<td>Vocabulary Extension</td>
<td>PROV-O</td>
</tr>
@@ -528,7 +527,7 @@
</tr>
<tr id="65">
<td>65</td>
- <th scope="row"><a href="http://provenance.ecs.soton.ac.uk/validator/validator.html">ProvValidator</a></th>
+ <th scope="row"><a href="http://provenance.ecs.soton.ac.uk/validator/validator.html">Prov-Validator</a></th>
<td>Validator</td>
<td>PROV-O, PROV-N, PROV-XML, PROV-JSON</td>
</tr>
@@ -2258,7 +2257,7 @@
<th scope="col"><a href="#45" title="roevo">#45</a></th>
<th scope="col"><a href="#46" title="wfprov">#46</a></th>
<th scope="col"><a href="#47" title="P-plan">#47</a></th>
- <th scope="col"><a href="#48" title="Jun Zhao">#48</a></th>
+ <th scope="col"><a href="#48" title="Provenance Vocabulary Core Ontology Specification">#48</a></th>
<th scope="col"><a href="#49" title="Systems molecular biology provenance ontology (SysPro) ">#49</a></th>
<th scope="col"><a href="#50" title="Yanfeng Shu">#50</a></th>
<th scope="col"><a href="#51" title="ISO_19115_Lineage">#51</a></th>
@@ -3333,9 +3332,9 @@
</caption>
<tr>
<th scope="col">Constraint</th>
- <th scope="col"> <a href="#64" title="prov-check">#62</a></th>
- <th scope="col"><a href="#65" title="checker.pl">#63</a></th>
- <th scope="col"><a href="#66" title="ProvValidator">#64</a></th>
+ <th scope="col"> <a href="#64" title="prov-check">#64</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
+ <th scope="col"><a href="#66" title="checker.pl">#66</a></th>
</tr>
<tr>
<td class="feature"><a href="http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html#key-object">Constraint 22 (key-object)</a></td>
@@ -3570,7 +3569,7 @@
<th scope="col">Provenenane Server</th>
<th scope="col">APROVeD</th>
<th scope="col">PROV Python</th>
- <th scope="col">ProvValidator</th>
+ <th scope="col">Prov-Validator</th>
<th scope="col">PROV-DM</th>
</tr>
<tr><td colspan=9></td></tr>
@@ -3586,7 +3585,7 @@
<td> </td>
</tr>
<tr>
- <th scope="row"><a href="#65">ProvValidator</a></th>
+ <th scope="row"><a href="#65">Prov-Validator</a></th>
<td> </td>
<td><span class="independent-impl">All (PROV-O)</span></td>
<td><span class="independent-codebase">All (PROV-N)</span></td>
@@ -3609,8 +3608,8 @@
</table>
<p>Summary:</p>
<ul>
- <li>The Provenance Server (University of Southampton, Python code base) consumes provenance documents deposited by the ProvToolbox Converter and ProvValidator (University of Southampton, Java code base)</li>
- <li>The ProvValidator (University of Southampton) validates:
+ <li>The Provenance Server (University of Southampton, Python code base) consumes provenance documents deposited by the ProvToolbox Converter and Prov-Validator (University of Southampton, Java code base)</li>
+ <li>The Prov-Validator (University of Southampton) validates:
<ul>
<li>All PROV-O terms generated by PROVoKing (King's College London)</li>
<li>All PROV-N terms generated by the Provenance Server and the PROV-Python library (University of Southampton, Python code base)</li>
@@ -3637,11 +3636,11 @@
</tr>
<tr>
<th scope="col">Consumer:</th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
<th scope="col"><a href="#64" title="prov-check">#64</a></th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
- <th scope="col"><a href="#65" title="ProvValidator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
+ <th scope="col"><a href="#65" title="Prov-Validator">#65</a></th>
</tr>
<tr>
<th scope="col">Term</th>
@@ -3996,7 +3995,7 @@
<td>2</td>
</tr>
</table>
- <p class="note">Although the Provenance Server (#17) and the ProvValidator (#65) are from the same institution (i.e. University of Southampton), it is worth noting that they were built from two independent code bases (one in Python and the other in Java)</p>
+ <p class="note">Although the Provenance Server (#17) and the Prov-Validator (#65) are from the same institution (i.e. University of Southampton), it is worth noting that they were built from two independent code bases (one in Python and the other in Java)</p>
</section>
<section class="appendix">
--- a/semantics/prov-sem.html Sun Apr 14 19:43:18 2013 +0200
+++ b/semantics/prov-sem.html Sun Apr 14 19:44:18 2013 +0200
@@ -92,6 +92,12 @@
border: 1px solid #888;
background: #fff;
}
+.lemma {
+ padding: 1em;
+ margin: 1em 0em 0em;
+ border: 1px solid #888;
+ background: #fff;
+}
.proof {
padding: 1em;
@@ -620,7 +626,7 @@
function updateRules() {
var count=1;
- $('.constraint,.definition,.inference,.semantics,.component,.theorem').each(function(index) {
+ $('.constraint,.definition,.inference,.semantics,.component,.theorem,.lemma').each(function(index) {
var myid=$(this).attr('id');
var mycount=$(this).attr('number');
@@ -911,8 +917,6 @@
// if you wish the publication date to be other than today, set this
publishDate: "2013-04-30",
- previousPublishDate: "2013-03-12",
- previousMaturity: "WD",
// if the specification's copyright date is a range of years, specify
// the start date here:
@@ -920,9 +924,11 @@
// if there is a previously published draft, uncomment this and set its YYYY-MM-DD date
// and its maturity status
-
+ previousPublishDate: "2013-03-12",
+ previousMaturity: "WD",
+
// if there a publicly available Editor's Draft, this is the link
- edDraftURI: "http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html",
+//edDraftURI: "http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html",
@@ -937,7 +943,7 @@
// only "name" is required
editors: [
{ name: "James Cheney", url:
- "http://homepages.inf.ed.ac.uk/jcheney", company:
+ "http://homepages.inf.ed.ac.uk/jcheney/", company:
"University of Edinburgh" },
],
@@ -985,10 +991,10 @@
<p> This document presents a model-theoretic semantics for the PROV
-data model (called the <dfn>naive semantics</dfn>), viewing
+data model, viewing
PROV-DM statements as atomic formulas in the sense of first-order
logic, and viewing the constraints and inferences specified in
-PROV-CONSTRAINTS as a first-order theory. It is shown that valid PROv
+PROV-CONSTRAINTS as a first-order theory. It is shown that valid PROV
instances (in the sense of PROV-CONSTRAINTS) correspond to satisfiable
theories.
This information may be useful to researchers or users of PROV to
@@ -1020,7 +1026,7 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [[PROV-XML]];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), the mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV and Dublic Core Terms [[PROV-DC]];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV and Dublin Core Terms [[PROV-DC]];</li>
<li> <a
href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a>
(Note), a declarative specification in terms of
@@ -1028,6 +1034,16 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
</ul>
+<h4>Implementations Encouraged</h4>
+<p>
+The Provenance Working Group encourages implementations that make use
+of or extend the semantics in this document.
+Although work on this document by the Provenance Working Group is complete,
+errors may be recorded in the <a href="http://www.w3.org/2011/prov/errata.html">errata</a> or and these may be addressed in future revisions.
+</p>
+
+<h4>Please Send Comments</h4>
+
</section>
@@ -1037,14 +1053,16 @@
<h2>Introduction</h2>
<p>
-Provenance is a record that describes the people, institutions, entities, and activities involved in producing, influencing, or delivering a piece of data or a thing.
+Provenance is a record that describes the people, institutions,
+entities, and activities involved in producing, influencing, or
+delivering a piece of data or a thing. [[PROV-DM]]
This document complements
the PROV-DM specification [[PROV-DM]] that defines a data model for
provenance on the Web, and the PROV-CONSTRAINTS specification
[[PROV-CONSTRAINTS]] that
specifies definitions, inferences, and constraints that can be used to
reason about PROV documents, or determine their validity. This document
-provides a naive formal semantics of PROV, providing a formal
+provides a formal semantics of PROV, providing a formal
counterpart to the informal descriptions and motivations given
elsewhere in PROV specifications.</p>
@@ -1072,7 +1090,7 @@
</section>
<p>The PROV-DM and PROV-CONSTRAINTS specifications give motivating examples that
provide an intuition about the meaning of the constructs. For some
-concepts, such as use, start, end, generation/invalidation, and
+concepts, such as use, start, end, generation, invalidation, and
derivation, the meaning is either obvious or situation-dependent.
However, during the development of PROV, the importance of additional
concepts became evident, but the intuitive meaning or correct use of
@@ -1092,27 +1110,27 @@
logic, principally model theory (though our use of these tools is lightweight). This information may be useful to users for understanding the
intent behind certain features of PROV, to researchers investigating
richer forms of reasoning over provenance, or to future efforts
-building upon PROV. It is intended as an exploration of <b>one</b> semantics for PROV, not a definitive specification of the <b>only</b>
+building upon PROV. It is intended as an exploration of <b>one</b> semantics for PROV, <b>not</b> a definitive specification of the <b>only</b>
semantics of PROV. We provide a semantics that satisfies all
of the constraints on valid PROV instances, and such that valid PROV
instances correspond to satisfiable theories: every valid instance has
a model, and vice versa.</p>
-<p> Although it is a work in progress, the naive semantics has some appealing
+<p> The semantics has some appealing
properties. Specifically, it provides a declarative counterpart to
the operational definition of validity taken in PROV-CONSTRAINTS. In
the specification, validity is defined via a normalization process
followed by constraint checking on the normal form. This approach was adopted
to keep the specification closer to implementations, although other
implementations are possible and allowed. In addition to providing a
-naive semantics, this document shows that the operational
+semantics, this document shows that the operational
presentation of PROV validity checking is equivalent to the
declarative presentation adopted here. This could help justify
alternative approaches to validity checking.</p>
<p>This document mostly considers the semantics of PROV statements and
instances. PROV documents can consist of multiple instances, such
- as named bundles. The semantics does not (as yet) cover general PROV documents, but the
+ as named bundles. The semantics do not cover general PROV documents, but the
semantics can be used on each instance in a document separately,
just as PROV-CONSTRAINTS specifies that each instance in a document
is to be validated separately.
@@ -1121,7 +1139,16 @@
The semantics of extensions of PROV, such as dictionaries
[[PROV-DICTIONARY]] and linking across bundles [[PROV-LINKS]], are
beyond the scope of this document. </p>
-
+
+
+<p>This document has been reviewed by the Working Group, but the
+theorems and proofs have not been
+formally peer-reviewed in the sense of an academic paper. Thus,
+the Working Group believes this document is an appropriate starting
+point for future study of the semantics of PROV, but further work may
+be needed.
+</p>
+
<section> <h4>Structure of this document</h4> <p>
</p>
@@ -1143,7 +1170,7 @@
<li><a href="#soundness-completeness">Section 6</a> summarizes the
main results relating PROV-CONSTRAINTS validation to the semantics,
including soundness and a weak form of completeness: a PROV
- instance is valid if and only if it has a naive model.</li>
+ instance is valid if and only if it has a model.</li>
</ul>
@@ -1224,7 +1251,7 @@
<h3> Identifiers </h3>
<p>A lowercase symbol $x,y,...$ on its own denotes an identifier.
-Identifiers may or may not be URIs. Identifiers are viewed as
+ Identifiers are viewed as
variables from the point of view of logic. Identifiers denote objects, and
two different identifiers $x$ and $y$ may denote equal or different objects. We write $Identifiers$ for the
set of identifiers of interest in a given situation (typically, the
@@ -1238,7 +1265,9 @@
<p>We assume a set $Attributes$ of attribute labels and a set $Values$
of possible values of attributes. To allow for the fact that some
attributes can have undefined or multiple values, we sometimes use the set
-$P(Value)$, that is, the set of sets of values.
+$P(Values)$, that is, the set of sets of values. Thus, we can use the
+empty set to stand for an undefined value and $\{a,b\}$ to stand for
+the set of values of a two-valued attribute.
</p> </section>
@@ -1247,7 +1276,7 @@
<h3> Times </h3>
<p>We assume an ordered set $(Times,\leq)$ of time instants, where
-$Times \subseteq Val$ and $\leq$ is a linear order.
+$Times \subseteq Values$ and $\leq$ is a linear order.
</p>
<!--
@@ -1255,7 +1284,7 @@
<p>Restricting attention to linearly-ordered times, and imposing this
order on events, is a simplifying assumption; it is more restrictive than required to model the
constraints. As a result, there are currently some valid PROV
- instances that do not have naive models. It is intended that the
+ instances that do not have models. It is intended that the
final version of the semantics will provide a more general class of
models such that every valid instance has a model.
</p>
@@ -1280,8 +1309,8 @@
<p>The following atomic formulas correspond to the statements of PROV-DM. We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation $r(id,a_1,\ldots,a_n)$ instead of the semicolon notation $r(id;a_1,\ldots,a_n)$.
</p>
<p>Each parameter is either an identifier, a constant (e.g. a time or
- other literal value in an attribute list), or a null symbol "-".
- Placeholder symbols $-$ can only appear in the specified arguments
+ other literal value in an attribute list), or a null symbol "$-$".
+ Placeholder symbols "$-$" can only appear in the specified arguments
$pl$ in $wasAssociatedWith$ and $a,g,u$ in $wasDerivedFrom$, as shown in the grammar below.
</p>
$$
@@ -1396,14 +1425,20 @@
interpret PROV formulas and instances. A structure consists of a
collection of sets, functions and relations. The components of a
structure $W$ are given in the rest of the section in
-<em>components</em>, highlighted in boxes.
-
+<em>components</em>, highlighted in boxes.</p>
+
+<div class="remark">
+ <p>We use the term "component" here in a different sense than in
+ PROV-DM. Here, the components are parts of a large definition,
+ whereas PROV-DM defines six components that group different parts of
+ the PROV data model.</p>
+ </div>
<section>
<h3> Things </h3>
<p><em>Things</em> is a set of things in the situation being modeled.
-Each thing has an associates set of $Events$ and attributes whose
+Each thing has an associated set of $Events$ and attributes whose
values can change over time. Different kinds of $Events$ are specified further below.
</p>
<p>To model this, a structure $W$ includes:
@@ -1412,7 +1447,7 @@
<li> a set $Things$ of things</li>
<li> a set $Events$ of events</li>
<li> a function $events : Things \to P(Events)$ from things to
- sets of events.</li>
+associated sets of events.</li>
<li>a function $value : Things \times Attributes \times Events \to
P(Values)$ giving the possible values of each attribute of a
$Thing$ at the instant of a given event.
@@ -1442,6 +1477,10 @@
Events$ and $a \in Attributes$, this does not imply that $T_0 = T_1$.
</p>
+<p>$Things$ are associated with certain kinds of $Objects$ called $Entities$, defined in
+the next subsection. Specifically, the function $thingOf$ associates
+an $Entity$ to a $Thing$.
+</p>
</section>
@@ -1485,7 +1524,7 @@
<p>As with <em>Things</em>, the range of $value$ is sets of values,
making $value$ effectively a multivalued function. It is also
possible to have two different objects that are indistinguishable by
-their attributes and time intervals. Objects are not things, and the
+their attributes and associated events. Objects are not things, and the
sets of $Objects$ and $Things$ are disjoint; however, certain objects,
namely entities, are associated with things.
</p>
@@ -1587,9 +1626,8 @@
<em>collections</em>, with the following associated structure:</p>
<div class="component" id="collections">
<ul><li>A set $Collections \subseteq Entities$</li>
- <li>A membership relation $Contains\subseteq Collections \times Entities$
- indicating when an entity is a member of another (collection)
- entity.</li>
+ <li>A membership function $members : Collections \to P( Entities)$
+mapping each collection to its set of members.</li>
</ul>
</div>
</section>
@@ -1599,7 +1637,8 @@
<h4> Activities </h4>
-<p>An <em>activity</em> is an object that encompasses a set of events. We introduce:
+<p>An <em>activity</em> is an object corresponding to a continuing
+ process rather than an evolving thing. We introduce:
</p>
<div class="component" id="activities">
<ol><li>A set $Activities \subseteq Objects$ of activities.</li>
@@ -1661,8 +1700,8 @@
<section>
<h5> Events </h5>
-<p>An $Event$ is an influence whose events is a single time
-instant, and relates an activity to an entity (which could be an
+<p>An $Event$ is an instantaneous influence that relates an activity
+to an entity (either of which could also be an
agent). Events have types including usage, generation, invalidation, starting and ending. Events are instantaneous. We introduce:
</p>
<div class="component" id="events">
@@ -1676,7 +1715,7 @@
\not\preceq e$ hold.
</li>
<li>A function $started : Starts \to Activities \times Entities \times
-Activities$, such that $started(st) = (a,e,a')$ implies $start \in
+Activities$, such that $started(start) = (a,e,a')$ implies $start \in
events(a) \cap events(e) \cap events(a')$.
</li>
<li>A function $ended : Ends \to Activities \times Entities \times Activities$, such that $ended(end) = (a,e,a')$ implies $end \in
@@ -1797,7 +1836,7 @@
and use step. However, not all such potential derivation paths are associated
with derivations; there can (and in general will) be many such paths
that are not associated with derivation steps. In other words, because we require derivations to be
- explicitly assocated with derivation paths, it is not sound to infer
+ explicitly associated with derivation paths, it is not sound to infer
the existence of a derivation from the existence of an
alternating generation/use chain.
</p>
@@ -1805,8 +1844,8 @@
The reason why we need paths and not just individual derivation
steps is to reflect that $wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)$ formulas can
represent multiple derivation steps. However, there is no way to
- express a multi-step derivation path in PROV: any valid PROV
- instance turns out to have a model in which all derivation paths are
+ force a derivation to take multiple steps. Any valid PROV
+ instance has a model in which all derivation paths are
one-step.</p></div>
</section>
@@ -1841,11 +1880,13 @@
</li>
<li id="axiom5">
If $d \in Derivations$ and $prov:Revision \in
- value(d,prov:type)$ and $derivationPath(deriv) = e_2 \cdot w \cdot
- e_1$ then $thingOf(e_1) = thingOf(e_2)$.
+ value(d,prov:type)$ and there exists $w \in (Generations \cup
+ Activities \cup Uses \cup Entities)^* $ such that $derivationPath(deriv) = e_2 \cdot w \cdot
+ e_1 \in DerivationPaths$ then $thingOf(e_1) = thingOf(e_2)$.
</li>
<li id="axiom6">
- If $attributedTo(att) = (e,ag)$ then there exist $gen$ and $assoc$
+ If $attributedTo(att) = (e,ag)$ then there exist $gen$, $assoc$
+ and $a$
such that $generated(gen) = (e,a)$ and $associatedWith(assoc) = (a,ag)$.
</li>
<li id="axiom7">
@@ -1957,8 +1998,7 @@
</li>
<li id="axiom36">
If $e \in Entity$ and $prov:emptyCollection \in
- value(e,prov:type)$ then $e \in Collections$ and there exists no
- $e'$ such that $(e,e') \in Contains$.
+ value(e,prov:type)$ then $e \in Collections$ and $members(e) = \emptyset$.
</ol>
</div>
@@ -1975,7 +2015,11 @@
should be a constraint analogous to Constraint 34 that specifies
that any invalidation event in which an activity participates must
follow the activity's start event(s) and precede its end
- event(s).</p>
+ event(s).
+ </p>
+ <p>Here, we exempt invalidations from axioms 22 and 23 in order to
+ simplify the proof of weak completeness.</p>
+
</div>
</section>
@@ -2157,14 +2201,14 @@
<li>[WF] The identifier $id$ maps to an activity $act = \rho(id) \in Activities$.
</li>
<li>$\rho(st) \in Times$ is the activity's start time, that is:
-$startTime(id) = \rho(st)$.
+$startTime(act) = \rho(st)$.
</li>
-<li>$\rho(et)$ is the activity's end time, that is: $endTime(id) = \rho(et)$.
+<li>$\rho(et)$ is the activity's end time, that is: $endTime(act) = \rho(et)$.
</li>
<li>There exists $start,e,a$ such that $started(start) = (act,e,a)$,
-and for all such start events $startTime(a) = time(start).</li>
+and for all such start events $startTime(act) = time(start).</li>
<li>There exists $end,e',a'$ such that $ended(end) = (act,e',a')$, and
-for all such end events $endTime(a) = time(end)$.</li>
+for all such end events $endTime(act) = time(end)$.</li>
<li>The attributes match: $match(W,act,attrs)$.
</li>
</ol>
@@ -2534,7 +2578,7 @@
<!--<li>$(ent_1,ent_2) \in SpecializationOf$.-->
<li>The two entities present aspects of the same thing, that is, $thingOf(ent_1) = thingOf(ent_2)$.
</li>
-<li>The events of $ent_1$ is contained in that of $ent_2$, i.e. $events(ent_1) \subseteq events(ent_2)$.
+<li>The events of $ent_1$ are contained in those of $ent_2$, i.e. $events(ent_1) \subseteq events(ent_2)$.
</li>
<li>For each attribute $attr$ we have $value(ent_1,attr) \supseteq value(ent_2,attr)$.</li>
<li>At least one of these inclusions is strict: that is, either
@@ -2557,7 +2601,7 @@
-->
<p>The second criterion says that the two Entities present (possibly different) aspects of
the same Thing. Note that the third criterion allows $ent_1$ and
-$ent_2$ to have the same events (or that of $ent_2$ can be larger).
+$ent_2$ to have the same events (or $events(ent_2)$ can be larger).
The last criterion allows $ent_1$ to have more defined attributes than
$ent_2$, but they must include the attributes defined by $ent_2$. Two
different entities that have the same attributes can also be related
@@ -2600,7 +2644,7 @@
= \rho(c) \in Collections$ and $ent = \rho(e) \in Entities$.
</li>
<li>The entity $ent$ is a member of the collection $coll$: that is,
-$(coll,ent) \in Contains$.
+$ent \in members(coll)$.
</li></ol>
</div>
@@ -2658,7 +2702,7 @@
<section>
<h4>notNull</h4>
<p>The $notNull(x)$ formula is used to specify that a value may not
- be the null value $\bot$. The symbol $-$ always denotes the null
+ be the null value $\bot$. The symbol "$-$" always denotes the null
value (i.e. $\rho(-) = \bot$).
<div class="semantics" id="notNull-semantics">
<p>$W,\rho\models notNull(e)$ holds if and only if $\rho(e) \neq
@@ -2684,8 +2728,7 @@
<li>$W,\rho\models typeOf(c,Collection)$ holds if and only if
$\rho(c) \in Collections$.</li>
<li>$W,\rho\models typeOf(c,EmptyCollection)$ holds if and only if
- $\rho(c) \in Collections$ and there is no $e \in Entities$ such
- that $(\rho(c),e) \in Contains$.</li>
+ $\rho(c) \in Collections$ and $members(\rho(c)=\emptyset$.</li>
</ol>
</div>
@@ -2702,7 +2745,7 @@
In this section we restate all of the inferences and constraints
of PROV-CONSTRAINTS in terms of first-order logic. For each, we
give a proof sketch showing why the inference or constraint is
- sound for reasoning about the naive semantics. We exclude the
+ sound for reasoning about the semantics. We exclude the
definitional rules in PROV-CONSTRAINTS because they are only
needed for expanding the abbreviated forms of PROV-N statements to
the logical formulas used here.</p>
@@ -3729,7 +3772,7 @@
<div class="proof">
<p>Each part follows from the fact that the semantics of
$wasDerivedFrom$ only allows formulas to hold when either all three
- of $a,g,u$ are $-$ (denoting $\bot$) or none of them are.</p>
+ of $a,g,u$ are "$-$" (denoting $\bot$) or none of them are.</p>
</div>
<div class="constraint" number="52" id="impossible-specialization-reflexive">$\begin{array}[t]{l}
\forall e.~
@@ -3812,7 +3855,7 @@
<h2>Soundness and Completeness</h2>
<p>Above we have presented arguments for the soundness of the
-constraints and inferences with respect to the naive semantics.
+constraints and inferences with respect to the semantics.
Here, we relate the notions of <dfn>validity</dfn> and <dfn>normal
form</dfn> defined in PROV-CONSTRAINTS to the semantics.
</p>
@@ -3863,8 +3906,31 @@
<h3>Weak Completeness</h3>
<p> In this section we give a translation from valid PROV instances to
- structures, and show that a valid PROV instance has a model.</p>
-
+ structures, and show that a valid PROV instance has a model. We
+ call this property <em>weak completeness</em>.
+
+ </p>
+
+ <div class="remark">
+ <p> The term <em>weak</em> refers to the fact that
+ there are still some inferences that are sound in the semantics but not
+ enforced by validation. For example, consider the following
+ (valid) PROV instance fragment:</p>
+ <pre>
+entity(e,[a=1])
+agent(e,[b=2])
+ </pre>
+ <p>This instance is valid and has a model, but in every model
+ satisfying the instance, it is also true that:</p>
+ <pre>
+entity(e,[a=1,b=2])
+agent(e,[a=1,b=2])
+ </pre>
+ <p>Thus, weak completeness captures the fact that every valid
+ instance has a model, but does not imply that a valid instance
+ satisfies all of the deductions possible in that model.
+ </p>
+ </div>
<p> Let $I$ be a valid PROV instance that is in normal form.
We define a structure $M(I)$ as follows, by giving the sets,
@@ -3874,49 +3940,71 @@
<p>First, without loss of generality, we assume that all times
specified in activity or event formulas in $I$ are ground values.
- If not, set each variable in such a position to some dummy value.</p>
-
+ If not, set each variable in such a position to some dummy value.
+ This is justified by the following fact:</p>
+
+<div class="lemma" id="time-grounding">
+ <p>
+ If $I$ is valid then $S(I)$ is valid, where $S$ is any
+ substitution that maps time variables to time constants.
+ </p>
+ </div>
+ <div class="proof">
+ <p>
+ First, consider a substitution $S = [t:=c]$ that maps a
+ single time variable to a constant. It is straightforward to check
+ that if $I$ is in normal form, then $S(I)$ is in normal form, since
+ none of the inferences or uniqueness constraints can be enabled by
+ changing a time variable uniformly in $I$. Similarly, the remaining
+ constraints are insensitive to the time values, so $S(I)$ is in
+ normal form and satisfies all of the remaining constraints just as
+ $I$ does. The general case of a substitution that replaces multiple time variables
+ with constants is a straightforward generalization since we can view
+ such a substitution as a composition of single-variable substitutions.
+ </p>
+ </div>
+
<section>
<h4>Sets</h4>
<p> The sets of structure $M(I)$ are: </p>
\[
\begin{eqnarray*}
Entities &=& \{id \mid I \models typeOf(id,entity)\}\\
- Plans &=& \{pl \mid wasAssociatedWith(id,ag,act,pl,attrs) \in I, pl
+ Plans &=& \{pl \mid \exists id,ag,ac,attrs.~ wasAssociatedWith(id,ag,act,pl,attrs) \in I, pl
\neq -\}\\
Collections &=& \{c \mid I \models typeOf(c,prov:Collection) \text{
or } I \models typeOf(c,prov:EmptyCollection)\} \\
Activities &=& \{id \mid I \models typeOf(id, activity)\}\\
&\cup& \{a_{id},a'_{id} \mid id \in Entities\}\\
- &\cup& \{a_{id} \mid wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in I\}\\
+ &\cup& \{a_{id} \mid \exists id,e_2,e_1.~wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in I\}\\
Agents &=& \{id \mid I \models typeOf(id,agent)\}\\
\\
- Usages &=& \{id \mid used(id,a,e,t,attrs) \in I\}\\
- &\cup& \{u_{id} \mid wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
+ Usages &=& \{id \mid \exists a,e,t,attrs.~used(id,a,e,t,attrs) \in I\}\\
+ &\cup& \{u_{id} \mid \exists id,e_2,e_1,attrs.~wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
I\}\\
- Generations &=& \{id \mid wasGeneratedBy(id,e,a,t,attrs) \in I\}\\
- &\cup& \{g_{id} \mid wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
+ Generations &=& \{id \mid \exists e,a,t,attrs.~wasGeneratedBy(id,e,a,t,attrs) \in I\}\\
+ &\cup& \{g_{id} \mid \exists id,e_2,e_1,attrs.~wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
I\}\\
& \cup & \{g_{id} \mid id \in Entities\}\\
- Invalidations &=& \{id \mid wasInvalidatedBy(id,e,a,t,attrs) \in
+ Invalidations &=& \{id \mid \exists e,a,t,attrs.~wasInvalidatedBy(id,e,a,t,attrs) \in
I\}\\
& \cup & \{i_{id} \mid id \in Entities\}\\
- Starts &=& \{id \mid wasStartedBy(id,a,e,a',t,attrs) \in I\}\\
- Ends &=& \{id \mid wasEndedBy(id,a,e,a',t,attrs) \in I\}\\
+ Starts &=& \{id \mid \exists a,e,a',t,attrs.~wasStartedBy(id,a,e,a',t,attrs) \in I\}\\
+ Ends &=& \{id \mid \exists a,e,a',t,attrs.~wasEndedBy(id,a,e,a',t,attrs) \in I\}\\
Events &=& Usages \cup Generations \cup Invalidations \cup Starts
\cup Ends\\
\\
- Associations &=& \{id \mid wasAssociatedWith(id,ag,act,pl,attrs) \in
+ Associations &=& \{id \mid \exists ag,act,pl,attrs.~ wasAssociatedWith(id,ag,act,pl,attrs) \in
I\}\\
- Attributions &=& \{id \mid wasAttributedTo(id,e,ag,attrs) \in I\}\\
- Delegations &=& \{id \mid actedOnBehalfOf(id,ag_2,ag_1,act,attrs) \in I\}\\
- Communications &=& \{id \mid wasInformedBy(id,a_2,a_1,attrs) \in I\}\\
- Derivations &=& \{id \mid wasDerivedFrom(id,e_2,e_1,a,g,u,attrs) \in I\}\\
+ Attributions &=& \{id \mid \exists e,ag,attrs.~wasAttributedTo(id,e,ag,attrs) \in I\}\\
+ Delegations &=& \{id \mid \exists ag_2,ag_1,attrs.~ actedOnBehalfOf(id,ag_2,ag_1,act,attrs) \in I\}\\
+ Communications &=& \{id \mid \exists a_2,a_1,attrs.~wasInformedBy(id,a_2,a_1,attrs) \in I\}\\
+ Derivations &=& \{id \mid \exists e_2,e_1,a,g,u,attrs.~wasDerivedFrom(id,e_2,e_1,a,g,u,attrs) \in I\}\\
\\
Influences &=& Events \cup Associations \cup Attributions \cup
Communications \cup Delegations\\
- &\cup & \{id \mid wasInfluencedBy(id,o_2,o_1,attrs) \in I\}\\
+ &\cup & \{id \mid \exists o_2,o_1,attrs.~ wasInfluencedBy(id,o_2,o_1,attrs) \in I\}\\
\\
Objects &=& Entities \cup Activities \cup Agents \cup Influences\\
\end{eqnarray*}
@@ -3986,7 +4074,7 @@
also define the set of all events involved in $e$ as the set of events
immediately involved in $e$ or any specialization of $e$. Similarly,
the values of attributes of $e$ are those immediately declared for $e$
-along with those of $e'$ that $e$ specializes. We also introduce dummy
+along with those of any $e'$ that $e$ specializes. We also introduce dummy
generation and invalidation events for each entity $e$, along with
activities $a_e,a'_e$ to perform them.
</p>
@@ -4059,7 +4147,7 @@
<p>This definition is deterministic because the sets of identifiers
of different $Events$ are disjoint, and the associated times are unique.</p>
- <p>Finally, the functions giving the interpretations of the
+ <p>The functions giving the interpretations of the
different identified influences are as follows:
</p>
\[\begin{eqnarray*}
@@ -4116,6 +4204,11 @@
<p> It is straightforward to verify (by their definitions) that the
event sets associated with entities and activities satisfy the
side-conditions in <a href="#events">Component 9</a>.</p>
+
+ <p> Finally, the collection membership function $members$ is
+ defined as follows:</p>
+ \[members(c) = \{e \mid hadMember(c,e) \in I\]
+
</section>
<section>
<h4>Relations</h4>
@@ -4126,11 +4219,8 @@
\[evt \preceq evt' \iff (evt,evt') \in G_I\]
<p> closed under reflexivity and transitivity. Here, we are using a slight abuse of notation: we write $G_I$
for the directed graph that is used during validation of $I$ to
- test for cycles amond event ordering constraints. See Sec. 7.1 of PROV-CONSTRAINTS [[PROV-CONSTRAINTS]].</p>
-
- <p> Finally, the collection membership relation $Contains$ is
- defined as follows:</p>
- \[(c,e) \in Contains \iff hadMember(c,e) \in I\]
+ test for cycles among event ordering constraints. See Sec. 7.1 of PROV-CONSTRAINTS [[PROV-CONSTRAINTS]].</p>
+
</section>
<section>
@@ -4319,8 +4409,17 @@
<h2>Acknowledgements</h2>
<p>
-This document has been produced by the PROV Working Group, and its contents reflect extensive discussion within the Working Group as a whole.
+This document has been produced by the PROV Working Group, and its
+ contents reflect extensive discussion within the Working Group
+ as a whole. Thanks specifically to Khalid Belhajjame, Tom De
+ Nies, Paolo
+ Missier, Simon Miles, Luc Moreau, Satya Sahoo, Jan van den
+ Bussche, and Joachim Van
+ Herwegen for detailed feedback.</p>
+<p>
+We would also like to acknowledge <a href="http://www.dagstuhl.de">Schloss Dagstuhl - Leibniz Center for Informatics</a>, because significant progress was made on this document at <a href="http://www.dagstuhl.de/en/program/calendar/semhp/?semnr=12091">Dagstuhl Seminar 12091 (Principles of Provenance)</a> that took place from February 26 to March 2, 2012.
</p>
+
<p>Thanks also to Robin Berjon for the ReSPec.js specification writing
tool and to MathJax for their LaTeX-to-HTML conversion tools, both of
which aided in the preparation of this document.</p>
--- a/semantics/releases/NOTE-prov-sem-20130430/Overview.html Sun Apr 14 19:43:18 2013 +0200
+++ b/semantics/releases/NOTE-prov-sem-20130430/Overview.html Sun Apr 14 19:44:18 2013 +0200
@@ -91,6 +91,12 @@
border: 1px solid #888;
background: #fff;
}
+.lemma {
+ padding: 1em;
+ margin: 1em 0em 0em;
+ border: 1px solid #888;
+ background: #fff;
+}
.proof {
padding: 1em;
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- <body><div id="MathJax_Message" style="display: none; "></div><div class="head">
+ <body><div class="head">
<p>
<a href="http://www.w3.org/"><img width="72" height="48" src="http://www.w3.org/Icons/w3c_home" alt="W3C"></a>
@@ -758,9 +764,6 @@
<dd><a href="http://www.w3.org/TR/prov-sem/">http://www.w3.org/TR/prov-sem/</a></dd>
- <dt>Latest editor's draft:</dt>
- <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd>
-
@@ -770,7 +773,7 @@
<dt>Editor:</dt>
- <dd><a href="http://homepages.inf.ed.ac.uk/jcheney">James Cheney</a>, University of Edinburgh</dd>
+ <dd><a href="http://homepages.inf.ed.ac.uk/jcheney/">James Cheney</a>, University of Edinburgh</dd>
</dl>
@@ -800,9 +803,8 @@
</p>
- <hr>
-</div>
-
+</div><div id="MathJax_Message" style="display: none; "></div>
+<hr />
<section id="abstract" class="introductory"><h2>Abstract</h2>
<p>
Provenance is information about entities, activities, and people
@@ -814,10 +816,10 @@
<p> This document presents a model-theoretic semantics for the PROV
-data model (called the <dfn id="dfn-naive-semantics">naive semantics</dfn>), viewing
+data model, viewing
PROV-DM statements as atomic formulas in the sense of first-order
logic, and viewing the constraints and inferences specified in
-PROV-CONSTRAINTS as a first-order theory. It is shown that valid PROv
+PROV-CONSTRAINTS as a first-order theory. It is shown that valid PROV
instances (in the sense of PROV-CONSTRAINTS) correspond to satisfiable
theories.
This information may be useful to researchers or users of PROV to
@@ -856,13 +858,23 @@
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-xml-20130430/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">PROV-AQ</a> (Note), the mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">PROV-DICTIONARY</a> (Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">PROV-DC</a> (Note) provides a mapping between PROV and Dublin Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-sem-20130430/">PROV-SEM</a>
(Note), a declarative specification in terms of
first-order logic of the PROV data model (this document);</li>
<li> <a href="http://www.w3.org/TR/2013/NOTE-prov-links-20130430/">PROV-LINKS</a> (Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
</ul>
+<h4 id="implementations-encouraged">Implementations Encouraged</h4>
+<p>
+The Provenance Working Group encourages implementations that make use
+of or extend the semantics in this document.
+Although work on this document by the Provenance Working Group is complete,
+errors may be recorded in the <a href="http://www.w3.org/2011/prov/errata.html">errata</a> or and these may be addressed in future revisions.
+</p>
+
+<h4 id="please-send-comments">Please Send Comments</h4>
+
<p>
This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as a Working Group Note.
@@ -919,14 +931,16 @@
<!--OddPage--><h2><span class="secno">1. </span>Introduction</h2>
<p>
-Provenance is a record that describes the people, institutions, entities, and activities involved in producing, influencing, or delivering a piece of data or a thing.
+Provenance is a record that describes the people, institutions,
+entities, and activities involved in producing, influencing, or
+delivering a piece of data or a thing. [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>]
This document complements
the PROV-DM specification [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] that defines a data model for
provenance on the Web, and the PROV-CONSTRAINTS specification
[<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>] that
specifies definitions, inferences, and constraints that can be used to
reason about PROV documents, or determine their validity. This document
-provides a naive formal semantics of PROV, providing a formal
+provides a formal semantics of PROV, providing a formal
counterpart to the informal descriptions and motivations given
elsewhere in PROV specifications.</p>
@@ -954,7 +968,7 @@
</section>
<p>The PROV-DM and PROV-CONSTRAINTS specifications give motivating examples that
provide an intuition about the meaning of the constructs. For some
-concepts, such as use, start, end, generation/invalidation, and
+concepts, such as use, start, end, generation, invalidation, and
derivation, the meaning is either obvious or situation-dependent.
However, during the development of PROV, the importance of additional
concepts became evident, but the intuitive meaning or correct use of
@@ -974,27 +988,27 @@
logic, principally model theory (though our use of these tools is lightweight). This information may be useful to users for understanding the
intent behind certain features of PROV, to researchers investigating
richer forms of reasoning over provenance, or to future efforts
-building upon PROV. It is intended as an exploration of <b>one</b> semantics for PROV, not a definitive specification of the <b>only</b>
+building upon PROV. It is intended as an exploration of <b>one</b> semantics for PROV, <b>not</b> a definitive specification of the <b>only</b>
semantics of PROV. We provide a semantics that satisfies all
of the constraints on valid PROV instances, and such that valid PROV
instances correspond to satisfiable theories: every valid instance has
a model, and vice versa.</p>
-<p> Although it is a work in progress, the naive semantics has some appealing
+<p> The semantics has some appealing
properties. Specifically, it provides a declarative counterpart to
the operational definition of validity taken in PROV-CONSTRAINTS. In
the specification, validity is defined via a normalization process
followed by constraint checking on the normal form. This approach was adopted
to keep the specification closer to implementations, although other
implementations are possible and allowed. In addition to providing a
-naive semantics, this document shows that the operational
+semantics, this document shows that the operational
presentation of PROV validity checking is equivalent to the
declarative presentation adopted here. This could help justify
alternative approaches to validity checking.</p>
<p>This document mostly considers the semantics of PROV statements and
instances. PROV documents can consist of multiple instances, such
- as named bundles. The semantics does not (as yet) cover general PROV documents, but the
+ as named bundles. The semantics do not cover general PROV documents, but the
semantics can be used on each instance in a document separately,
just as PROV-CONSTRAINTS specifies that each instance in a document
is to be validated separately.
@@ -1003,7 +1017,16 @@
The semantics of extensions of PROV, such as dictionaries
[<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>] and linking across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>], are
beyond the scope of this document. </p>
-
+
+
+<p>This document has been reviewed by the Working Group, but the
+theorems and proofs have not been
+formally peer-reviewed in the sense of an academic paper. Thus,
+the Working Group believes this document is an appropriate starting
+point for future study of the semantics of PROV, but further work may
+be needed.
+</p>
+
<section id="structure-of-this-document"> <h3><span class="secno">1.2 </span>Structure of this document</h3> <p>
</p>
@@ -1025,7 +1048,7 @@
<li><a href="#soundness-completeness">Section 6</a> summarizes the
main results relating PROV-CONSTRAINTS validation to the semantics,
including soundness and a weak form of completeness: a PROV
- instance is valid if and only if it has a naive model.</li>
+ instance is valid if and only if it has a model.</li>
</ul>
@@ -1106,7 +1129,7 @@
<h3><span class="secno">2.1 </span> Identifiers </h3>
<p>A lowercase symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-3-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">,</mo><mi>y</mi><mo stretchy="false">,</mo><mo>.</mo><mo>.</mo><mo>.</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-3">x,y,...</script> on its own denotes an identifier.
-Identifiers may or may not be URIs. Identifiers are viewed as
+ Identifiers are viewed as
variables from the point of view of logic. Identifiers denote objects, and
two different identifiers <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-4-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-4">x</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-5-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-5">y</script> may denote equal or different objects. We write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-6-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-6">Identifiers</script> for the
set of identifiers of interest in a given situation (typically, the
@@ -1120,7 +1143,9 @@
<p>We assume a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-7-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-7">Attributes</script> of attribute labels and a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-8-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-8">Values</script>
of possible values of attributes. To allow for the fact that some
attributes can have undefined or multiple values, we sometimes use the set
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-9-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-9">P(Value)</script>, that is, the set of sets of values.
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-9-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-9">P(Values)</script>, that is, the set of sets of values. Thus, we can use the
+empty set to stand for an undefined value and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-10-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mi>a</mi><mo stretchy="false">,</mo><mi>b</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-10">\{a,b\}</script> to stand for
+the set of values of a two-valued attribute.
</p> </section>
@@ -1128,8 +1153,8 @@
<section id="times">
<h3><span class="secno">2.3 </span> Times </h3>
-<p>We assume an ordered set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-10-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mo stretchy="false">≤</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-10">(Times,\leq)</script> of time instants, where
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-11-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>V</mi><mi>a</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-11">Times \subseteq Val</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-12-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≤</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-12">\leq</script> is a linear order.
+<p>We assume an ordered set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-11-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mo stretchy="false">≤</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-11">(Times,\leq)</script> of time instants, where
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-12-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-12">Times \subseteq Values</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-13-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≤</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-13">\leq</script> is a linear order.
</p>
<!--
@@ -1137,7 +1162,7 @@
<p>Restricting attention to linearly-ordered times, and imposing this
order on events, is a simplifying assumption; it is more restrictive than required to model the
constraints. As a result, there are currently some valid PROV
- instances that do not have naive models. It is intended that the
+ instances that do not have models. It is intended that the
final version of the semantics will provide a more general class of
models such that every valid instance has a model.
</p>
@@ -1159,14 +1184,14 @@
<section id="formulas">
<h3><span class="secno">2.4 </span>Atomic Formulas</h3>
-<p>The following atomic formulas correspond to the statements of PROV-DM. We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-13-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-13">r(id,a_1,\ldots,a_n)</script> instead of the semicolon notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-14-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">;</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-14">r(id;a_1,\ldots,a_n)</script>.
+<p>The following atomic formulas correspond to the statements of PROV-DM. We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-14-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-14">r(id,a_1,\ldots,a_n)</script> instead of the semicolon notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-15-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">;</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-15">r(id;a_1,\ldots,a_n)</script>.
</p>
<p>Each parameter is either an identifier, a constant (e.g. a time or
- other literal value in an attribute list), or a null symbol "-".
- Placeholder symbols <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-15-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-15">-</script> can only appear in the specified arguments
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-16-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-16">pl</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-17-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-17">wasAssociatedWith</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-18-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-18">a,g,u</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-19-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-19">wasDerivedFrom</script>, as shown in the grammar below.
+ other literal value in an attribute list), or a null symbol "<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-16-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-16">-</script>".
+ Placeholder symbols "<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-17-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-17">-</script>" can only appear in the specified arguments
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-18-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-18">pl</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-19-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-19">wasAssociatedWith</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-20-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-20">a,g,u</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-21-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-21">wasDerivedFrom</script>, as shown in the grammar below.
</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-20-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi>a</mi><mi>t</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>c</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>e</mi><mi>l</mi><mi>e</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>r</mi><mi>e</mi><mi>l</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>u</mi><mi>x</mi><mi>i</mi><mi>l</mi><mi>i</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>l</mi><mi>e</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mi>e</mi><mi>l</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>f</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo 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stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>x</mi><mo stretchy="false">,</mo><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mi>u</mi><mi>x</mi><mi>i</mi><mi>l</mi><mi>i</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></mtd><mtd><mo stretchy="false">::=</mo></mtd><mtd><mo stretchy="false">[</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>n</mi></msub><mo stretchy="false">=</mo><msub><mi>v</mi><mi>n</mi></msub><mo stretchy="false">]</mo></mtd></mtr><mtr><mtd><mi>t</mi><mi>y</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-22">
\newcommand{\precedes}{~\mathrel{\textrm{precedes}}~}
\newcommand{\strictlyPrecedes}{~\mathrel{\textrm{strictlyPrecedes}}~}
\begin{array}{rcl}
@@ -1209,28 +1234,28 @@
</script>
<div class="remark">
- <p>We include the standard PROV collection types (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-21-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-21">Collection</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-22-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-22">EmptyCollection</script>) and the membership relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-23-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-23">hadMember</script>; however,
+ <p>We include the standard PROV collection types (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-23-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-23">Collection</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-24-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-24">EmptyCollection</script>) and the membership relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-25-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-25">hadMember</script>; however,
we do not model dictionaries or the insertion or deletion relations
in PROV-DICTIONARY [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>], since these are not part
of the PROV recommendations. If these features are incorporated
into future standards, their semantics (and the soundness of the
associated constraints) should be modeled.
- We omit the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-24-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-24">prov</script> prefixes from the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-25-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-25">Collection</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-26-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-26">EmptyCollection</script> types.
+ We omit the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-26-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-26">prov</script> prefixes from the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-27-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-27">Collection</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-28-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-28">EmptyCollection</script> types.
</p>
<p>As stated in the Introduction, we do not explicitly model
bundles or PROV documents; however, each instance can be viewed as
a set of formulas and can be modeled separately. The semantics of
the standard features of PROV can be defined without talking about
- multiple instances; however, the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-27-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-27">mentionOf</script> relation in
+ multiple instances; however, the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-29-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-29">mentionOf</script> relation in
PROV-LINKS [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>] is intended to support linking across
- bundles. Future editions of PROV may incorporate <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-28-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-28">mentionOf</script> or
+ bundles. Future editions of PROV may incorporate <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-30-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-30">mentionOf</script> or
other cross-instance assertions, and if so this semantics should be
generalized in order to provide a rationale for such an
extension and to establish the soundness of constraints associated
- with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-29-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-29">mentionOf</script>. </p>
+ with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-31-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-31">mentionOf</script>. </p>
</div>
</section>
@@ -1238,8 +1263,8 @@
<h3><span class="secno">2.5 </span>First-Order Formulas</h3>
<p>We also consider the usual connectives and quantifiers of
-first-order logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>].</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-30-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="italic">ϕ</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>a</mi><mi>t</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>c</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>x</mi><mo stretchy="false">=</mo><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">¬</mi><mtext> </mtext><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∨</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">⇒</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-30">
+first-order logic.</p>
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-32-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="italic">ϕ</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>a</mi><mi>t</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>c</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>x</mi><mo stretchy="false">=</mo><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">¬</mi><mtext> </mtext><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∨</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">⇒</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-32">
\begin{array}{rcl}
\phi &{::=}& atomic\_formula\\
& | & True\\
@@ -1274,56 +1299,66 @@
<section id="structures">
<!--OddPage--><h2><span class="secno">3. </span> Structures and Interpretations </h2>
-<p> In this section we define mathematical structures <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-31-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-31">W</script> that can be used to
+<p> In this section we define mathematical structures <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-33-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-33">W</script> that can be used to
interpret PROV formulas and instances. A structure consists of a
collection of sets, functions and relations. The components of a
-structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-32-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-32">W</script> are given in the rest of the section in
-<em>components</em>, highlighted in boxes.
-
-
-</p><section id="things-1">
+structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-34-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-34">W</script> are given in the rest of the section in
+<em>components</em>, highlighted in boxes.</p>
+
+<div class="remark">
+ <p>We use the term "component" here in a different sense than in
+ PROV-DM. Here, the components are parts of a large definition,
+ whereas PROV-DM defines six components that group different parts of
+ the PROV data model.</p>
+ </div>
+
+<section id="things-1">
<h3><span class="secno">3.1 </span> Things </h3>
<p><em>Things</em> is a set of things in the situation being modeled.
-Each thing has an associates set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-33-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-33">Events</script> and attributes whose
-values can change over time. Different kinds of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-34-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-34">Events</script> are specified further below.
+Each thing has an associated set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-35-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-35">Events</script> and attributes whose
+values can change over time. Different kinds of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-36-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-36">Events</script> are specified further below.
</p>
-<p>To model this, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-35-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-35">W</script> includes:
+<p>To model this, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-37-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-37">W</script> includes:
</p>
<div class="component" id="things" data-count="1" data-title="Component 1 (things)"><div class="ruleTitle"><a class="internalDFN" href="#things">Component 1 (things)</a></div><ol>
- <li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-36-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-36">Things</script> of things</li>
- <li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-37-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-37">Events</script> of events</li>
- <li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-38-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-38">events : Things \to P(Events)</script> from things to
- sets of events.</li>
- <li>a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-39-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-39">value : Things \times Attributes \times Events \to
+ <li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-38-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-38">Things</script> of things</li>
+ <li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-39-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-39">Events</script> of events</li>
+ <li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-40-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-40">events : Things \to P(Events)</script> from things to
+associated sets of events.</li>
+ <li>a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-41-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-41">value : Things \times Attributes \times Events \to
P(Values)</script> giving the possible values of each attribute of a
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-40-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-40">Thing</script> at the instant of a given event.
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-42-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-42">Thing</script> at the instant of a given event.
</li>
<li>Attributes are only defined during the events of a thing, that
-is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-41-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">≠</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-41">value(T,a,evt) \neq \emptyset</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-42-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-42">evt \in events(T)</script>.
+is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-43-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">≠</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-43">value(T,a,evt) \neq \emptyset</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-44-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-44">evt \in events(T)</script>.
</li></ol>
</div>
<p>
-The range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-43-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-43">value</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-44-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-44">P(Values)</script>, indicating that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-45-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-45">value</script>
-is essentially a multi-valued function that returns a set of values (possibly empty). When <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-46-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-46">value(x,a,evt) =
-\emptyset</script>, we say that attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-47-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-47">a</script> is undefined for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-48-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-48">x</script> at event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-49-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-49">evt</script>.</p>
+The range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-45-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-45">value</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-46-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-46">P(Values)</script>, indicating that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-47-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-47">value</script>
+is essentially a multi-valued function that returns a set of values (possibly empty). When <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-48-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-48">value(x,a,evt) =
+\emptyset</script>, we say that attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-49-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-49">a</script> is undefined for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-50-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-50">x</script> at event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-51-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-51">evt</script>.</p>
<p>Note that this description does not say what the structure of a
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-50-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-50">Thing</script> is, only how it may be described in terms of its events
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-52-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-52">Thing</script> is, only how it may be described in terms of its events
and attribute values. A thing could be a record of fixed
attribute values; it could be a bear; it could be the Royal Society;
-it could be a transcendental number like <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-51-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">π</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-51">\pi</script>. All that matters from
-our point of view is that we know how to map the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-52-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-52">Thing</script> to its events and attribute mapping.
+it could be a transcendental number like <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-53-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">π</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-53">\pi</script>. All that matters from
+our point of view is that we know how to map the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-54-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-54">Thing</script> to its events and attribute mapping.
</p>
<p>The identity of a Thing is not observable through its attributes or
-events, so it is possible for two different <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-53-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-53">Things</script> to be indistinguishable by their
-attribute values and events. That is, if the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-54-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>T</mi><mn>1</mn></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-54">Things = \{T_0,T_1\}</script> and the attributes are
-specified as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-55-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>T</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-55">value(T_0,a,evt) = value(T_1,a,evt)</script> for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-56-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-56">evt\in
-Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-57-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">∈</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-57">a \in Attributes</script>, this does not imply that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-58-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">=</mo><msub><mi>T</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-58">T_0 = T_1</script>.
+events, so it is possible for two different <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-55-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-55">Things</script> to be indistinguishable by their
+attribute values and events. That is, if the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-56-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>T</mi><mn>1</mn></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-56">Things = \{T_0,T_1\}</script> and the attributes are
+specified as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-57-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>T</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-57">value(T_0,a,evt) = value(T_1,a,evt)</script> for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-58-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-58">evt\in
+Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-59-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">∈</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-59">a \in Attributes</script>, this does not imply that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-60-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">=</mo><msub><mi>T</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-60">T_0 = T_1</script>.
</p>
+<p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-61-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-61">Things</script> are associated with certain kinds of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-62-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-62">Objects</script> called <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-63-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-63">Entities</script>, defined in
+the next subsection. Specifically, the function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-64-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-64">thingOf</script> associates
+an <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-65-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-65">Entity</script> to a <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-66-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-66">Thing</script>.
+</p>
</section>
@@ -1331,17 +1366,17 @@
<h3><span class="secno">3.2 </span> Objects </h3>
-<p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-59-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-59">Things</script> are things in the world that have attributes that
- can change over time. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-60-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-60">Things</script> may not have distinguishing features
+<p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-67-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-67">Things</script> are things in the world that have attributes that
+ can change over time. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-68-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-68">Things</script> may not have distinguishing features
that are readily observable and permanent. In PROV, we do not talk
- explicitly about <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-61-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-61">Things</script>, but instead we talk about various objects
+ explicitly about <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-69-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-69">Things</script>, but instead we talk about various objects
that have discrete, fixed features, and relationships among these
- objects. Some objects, called <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-62-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-62">Entities</script>, are associated with
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-63-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-63">Things</script>, and their fixed attributes need to match those of the
- associated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-64-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-64">Thing</script> during their common events. Others correspond
+ objects. Some objects, called <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-70-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-70">Entities</script>, are associated with
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-71-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-71">Things</script>, and their fixed attributes need to match those of the
+ associated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-72-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-72">Thing</script> during their common events. Others correspond
to agents, activities, or identifiable interactions among them.</p>
-<p>In this section, we detail the different subsets of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-65-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-65">Objects</script>, and
+<p>In this section, we detail the different subsets of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-73-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-73">Objects</script>, and
give disjointness constraints and associated functions. Generally, these constraints are necessary to validate
disjointness constraints from PROV-CONSTRAINTS [<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>].
</p>
@@ -1354,29 +1389,29 @@
</p>
<div class="component" id="objects" data-count="2" data-title="Component 2 (objects)"><div class="ruleTitle"><a class="internalDFN" href="#objects">Component 2 (objects)</a></div>
- <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-66-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-66">Objects</script>
-</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-67-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-67">events : Objects \to P(Events)</script> from objects
+ <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-74-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-74">Objects</script>
+</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-75-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-75">events : Objects \to P(Events)</script> from objects
to associated sets of events.
-</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-68-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-68">value : Objects \times Attributes \to P(Values)</script>.
+</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-76-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-76">value : Objects \times Attributes \to P(Values)</script>.
</li></ol>
</div>
-<p>Intuitively, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-69-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-69">events(e)</script> is the set of events in which <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-70-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-70">e</script> participated. The set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-71-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-71">value(e,a)</script> is the set of values of attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-72-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-72">a</script> during the object's events.
+<p>Intuitively, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-77-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-77">events(e)</script> is the set of events in which <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-78-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-78">e</script> participated. The set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-79-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-79">value(e,a)</script> is the set of values of attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-80-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-80">a</script> during the object's events.
</p>
-<p>As with <em>Things</em>, the range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-73-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-73">value</script> is sets of values,
-making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-74-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-74">value</script> effectively a multivalued function. It is also
+<p>As with <em>Things</em>, the range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-81-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-81">value</script> is sets of values,
+making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-82-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-82">value</script> effectively a multivalued function. It is also
possible to have two different objects that are indistinguishable by
-their attributes and time intervals. Objects are not things, and the
-sets of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-75-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-75">Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-76-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-76">Things</script> are disjoint; however, certain objects,
+their attributes and associated events. Objects are not things, and the
+sets of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-83-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-83">Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-84-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-84">Things</script> are disjoint; however, certain objects,
namely entities, are associated with things.
</p>
<div class="remark">
<p>
- Disjointness between <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-77-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-77">Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-78-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-78">Things</script> is not necessary but is
+ Disjointness between <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-85-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-85">Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-86-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-86">Things</script> is not necessary but is
assumed in order to avoid confusion between the different categories
- (time-varying <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-79-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-79">Things</script> vs fixed <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-80-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-80">Objects</script>).
+ (time-varying <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-87-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-87">Things</script> vs fixed <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-88-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-88">Objects</script>).
</p>
</div>
@@ -1387,11 +1422,11 @@
thing. We assume:</p>
<div class="component" id="entities" data-count="3" data-title="Component 3 (entities)"><div class="ruleTitle"><a class="internalDFN" href="#entities">Component 3 (entities)</a></div>
- <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-81-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-81">Entities \subseteq Objects</script> of entities, disjoint from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-82-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-82">Activities</script> below.
-</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-83-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-83">thingOf : Entities \to Things</script> that associates
- each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-84-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-84">Entity</script> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-85-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-85">e</script> with a <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-86-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-86">Thing</script>, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-87-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-87">events(e) \subseteq
- events(thingOf(e))</script> and for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-88-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-88">evt \in
- events(e)</script> and for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-89-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-89">a</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-90-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-90">value(e,a)
+ <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-89-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-89">Entities \subseteq Objects</script> of entities, disjoint from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-90-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-90">Activities</script> below.
+</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-91-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-91">thingOf : Entities \to Things</script> that associates
+ each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-92-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-92">Entity</script> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-93-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-93">e</script> with a <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-94-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-94">Thing</script>, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-95-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-95">events(e) \subseteq
+ events(thingOf(e))</script> and for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-96-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-96">evt \in
+ events(e)</script> and for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-97-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-97">a</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-98-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-98">value(e,a)
\subseteq value(thingOf(e),a,evt)</script>.
</li>
<!--<li>a relation $SpecializationOf \subseteq Entities \times Entities$
@@ -1411,44 +1446,44 @@
<div class="remark"><p> Although both entities and things can have
undefined or multiple attribute values, their meaning is slightly
- different: for a thing, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-91-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-91">value(x,a,evt) = \emptyset</script> means that the
- attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-92-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-92">a</script> has no value at event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-93-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-93">evt</script>, whereas for an entity,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-94-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-94">value(x,a) = \emptyset</script> only means that the thing associated to
- entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-95-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-95">x</script> need not have a
- fixed value for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-96-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-96">a</script> during the events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-97-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-97">x</script>. This does not imply
- that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-98-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-98">value(thingOf(e),a,evt) = \emptyset</script> when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-99-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-99">evt \in events(e)</script>.
+ different: for a thing, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-99-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-99">value(x,a,evt) = \emptyset</script> means that the
+ attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-100-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-100">a</script> has no value at event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-101-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-101">evt</script>, whereas for an entity,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-102-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-102">value(x,a) = \emptyset</script> only means that the thing associated to
+ entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-103-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-103">x</script> need not have a
+ fixed value for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-104-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-104">a</script> during the events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-105-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-105">x</script>. This does not imply
+ that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-106-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-106">value(thingOf(e),a,evt) = \emptyset</script> when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-107-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-107">evt \in events(e)</script>.
</p>
<p>Furthermore, all of the attribute values of the entity must
be present in the associated thing throughout the events of the
- entity. For example, suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-100-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-100">value(thingOf(e),a,evt)</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-101-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-101">\{1\}</script> at
- some event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-102-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-102"> evt \in events(e)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-103-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-103">value(thingOf(e),a,evt') = \{2\}</script> at
- some other event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-104-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-104">evt'</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-105-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-105">value(e,a)</script> must be <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-106-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-106">\emptyset</script> because
+ entity. For example, suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-108-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-108">value(thingOf(e),a,evt)</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-109-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-109">\{1\}</script> at
+ some event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-110-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-110"> evt \in events(e)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-111-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-111">value(thingOf(e),a,evt') = \{2\}</script> at
+ some other event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-112-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-112">evt'</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-113-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-113">value(e,a)</script> must be <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-114-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-114">\emptyset</script> because
there is no other set of values that is simultaneously contained in
- both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-107-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-107">\{1\}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-108-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-108">\{2\}</script>. </p> </div>
+ both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-115-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-115">\{1\}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-116-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-116">\{2\}</script>. </p> </div>
<div class="remark">
<p>
- In the above description of how <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-109-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-109">Entities</script> relate to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-110-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-110">Things</script>, we
- require <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-111-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-111">value(e,a) \subseteq
- value(thingOf(e),a,evt)</script> whenever <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-112-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-112">evt \in events(e)</script>. Intuitively, this means that if we are
- talking about a <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-113-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-113">Thing</script> indirectly by describing an <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-114-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-114">Entity</script>, then
- any attributes we ascribe to the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-115-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-115">Entity</script> must also describe the
- associated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-116-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-116">Thing</script> during their common events. Attributes of both
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-117-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-117">Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-118-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-118">Things</script> are multi-valued, so there is no
+ In the above description of how <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-117-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-117">Entities</script> relate to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-118-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-118">Things</script>, we
+ require <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-119-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-119">value(e,a) \subseteq
+ value(thingOf(e),a,evt)</script> whenever <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-120-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-120">evt \in events(e)</script>. Intuitively, this means that if we are
+ talking about a <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-121-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-121">Thing</script> indirectly by describing an <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-122-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-122">Entity</script>, then
+ any attributes we ascribe to the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-123-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-123">Entity</script> must also describe the
+ associated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-124-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-124">Thing</script> during their common events. Attributes of both
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-125-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-125">Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-126-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-126">Things</script> are multi-valued, so there is no
inconsistency in saying that an entity has two different values for
some attribute. In some
situations, further uniqueness constraints or range constraints
could be imposed on attributes.
</p>
- <p>Only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-119-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-119">Entities</script> are associated with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-120-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-120">Things</script>, and this
+ <p>Only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-127-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-127">Entities</script> are associated with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-128-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-128">Things</script>, and this
association is
- necessary to provide an interpretation for the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-121-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-121">alternateOf</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-122-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-122">specializationOf</script> relations. It might also make sense
- to associate <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-123-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-123">Agents</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-124-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-124">Activities</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-125-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-125">Interactions</script> with
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-126-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-126">Things</script>, or with some other structures; however, this is not
+ necessary to provide an interpretation for the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-129-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-129">alternateOf</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-130-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-130">specializationOf</script> relations. It might also make sense
+ to associate <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-131-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-131">Agents</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-132-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-132">Activities</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-133-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-133">Interactions</script> with
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-134-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-134">Things</script>, or with some other structures; however, this is not
necessary to model any of the current features of PROV, so in the
interest of simplicity we do not do this.
</p>
@@ -1459,7 +1494,7 @@
<p>We identify a specific subset of the entities called
<em>plans</em>:</p>
<div class="component" id="plans" data-count="4" data-title="Component 4 (plans)"><div class="ruleTitle"><a class="internalDFN" href="#plans">Component 4 (plans)</a></div>
- <p> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-127-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-127">Plans \subseteq Entities</script> of plans.</p>
+ <p> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-135-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-135">Plans \subseteq Entities</script> of plans.</p>
</div>
</section>
@@ -1468,10 +1503,9 @@
<p>We identify another specific subset of the entities called
<em>collections</em>, with the following associated structure:</p>
<div class="component" id="collections" data-count="5" data-title="Component 5 (collections)"><div class="ruleTitle"><a class="internalDFN" href="#collections">Component 5 (collections)</a></div>
- <ul><li>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-128-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-128">Collections \subseteq Entities</script></li>
- <li>A membership relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-129-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-129">Contains\subseteq Collections \times Entities</script>
- indicating when an entity is a member of another (collection)
- entity.</li>
+ <ul><li>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-136-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-136">Collections \subseteq Entities</script></li>
+ <li>A membership function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-137-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-137">members : Collections \to P( Entities)</script>
+mapping each collection to its set of members.</li>
</ul>
</div>
</section>
@@ -1481,13 +1515,14 @@
<h4><span class="secno">3.2.2 </span> Activities </h4>
-<p>An <em>activity</em> is an object that encompasses a set of events. We introduce:
+<p>An <em>activity</em> is an object corresponding to a continuing
+ process rather than an evolving thing. We introduce:
</p>
<div class="component" id="activities" data-count="6" data-title="Component 6 (activities)"><div class="ruleTitle"><a class="internalDFN" href="#activities">Component 6 (activities)</a></div>
- <ol><li>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-130-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-130">Activities \subseteq Objects</script> of activities.</li>
- <li>Functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-131-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-131">startTime : Activities \to Times</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-132-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-132">endTime
+ <ol><li>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-138-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-138">Activities \subseteq Objects</script> of activities.</li>
+ <li>Functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-139-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-139">startTime : Activities \to Times</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-140-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-140">endTime
:Activities \to Times</script> giving the start and end time of each activity.</li>
- <li> Activities are disjoint from Entities: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-133-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∩</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-133">Entities\cap Activities
+ <li> Activities are disjoint from Entities: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-141-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∩</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-141">Entities\cap Activities
= \emptyset</script>.</li>
</ol>
</div></section>
@@ -1504,7 +1539,7 @@
entities and activities are disjoint. We introduce:
</p>
<div class="component" id="agents" data-count="7" data-title="Component 7 (agents)"><div class="ruleTitle"><a class="internalDFN" href="#agents">Component 7 (agents)</a></div>
- <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-134-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-134">Agents \subseteq Objects</script> of agents.</p>
+ <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-142-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-142">Agents \subseteq Objects</script> of agents.</p>
</div>
<div class="remark">
<p>There is no requirement that every agent is either an activity
@@ -1515,26 +1550,26 @@
<section id="influences-1">
<h4><span class="secno">3.2.4 </span> Influences </h4>
-<p>We consider a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-135-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-135">Influences \subseteq Objects</script> which has disjoint
+<p>We consider a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-143-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-143">Influences \subseteq Objects</script> which has disjoint
subsets
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-136-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-136">Events</script> connecting entities and activities,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-137-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-137">Associations</script> between agents and activities,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-138-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-138">Attributions</script> between entities and agents,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-139-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-139">Communications</script> between pairs of activities,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-140-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-140">Delegations</script> between pairs of agents, and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-141-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-141">Derivations</script> that describe chains of generation and usage
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-144-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-144">Events</script> connecting entities and activities,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-145-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-145">Associations</script> between agents and activities,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-146-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-146">Attributions</script> between entities and agents,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-147-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-147">Communications</script> between pairs of activities,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-148-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-148">Delegations</script> between pairs of agents, and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-149-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-149">Derivations</script> that describe chains of generation and usage
steps. These kinds of influences are discussed further below. Influences are disjoint from entities, activities and agents.
</p>
<div class="component" id="influences" data-count="8" data-title="Component 8 (influences)"><div class="ruleTitle"><a class="internalDFN" href="#influences">Component 8 (influences)</a></div>
- <ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-142-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-142">Influences = Events \cup Associations \cup
+ <ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-150-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-150">Influences = Events \cup Associations \cup
Communications \cup Delegations \cup Derivations \subseteq Objects</script>
</li>
-<li> The sets <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-143-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-143">Events</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-144-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-144">Associations</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-145-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-145">Communications</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-146-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-146">Delegations</script>
- and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-147-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-147">Derivations</script> are all pairwise disjoint.
+<li> The sets <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-151-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-151">Events</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-152-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-152">Associations</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-153-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-153">Communications</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-154-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-154">Delegations</script>
+ and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-155-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-155">Derivations</script> are all pairwise disjoint.
</li><li> Influences are disjoint from entities, agents and
-activities: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-148-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∩</mo><mo stretchy="false">(</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-148">Influences \cap (Entities \cup Activities \cup Agents) = \emptyset</script>
+activities: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-156-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∩</mo><mo stretchy="false">(</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-156">Influences \cap (Entities \cup Activities \cup Agents) = \emptyset</script>
</li>
-<li>An associated function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-149-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-149">influenced : Influences \to
+<li>An associated function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-157-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-157">influenced : Influences \to
Objects \times Objects</script> giving the source and target of each influence.</li>
</ol>
</div>
@@ -1543,37 +1578,37 @@
<section id="events-1">
<h5><span class="secno">3.2.4.1 </span> Events </h5>
-<p>An <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-150-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-150">Event</script> is an influence whose events is a single time
-instant, and relates an activity to an entity (which could be an
+<p>An <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-158-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-158">Event</script> is an instantaneous influence that relates an activity
+to an entity (either of which could also be an
agent). Events have types including usage, generation, invalidation, starting and ending. Events are instantaneous. We introduce:
</p>
<div class="component" id="events" data-count="9" data-title="Component 9 (events)"><div class="ruleTitle"><a class="internalDFN" href="#events">Component 9 (events)</a></div>
-<ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-151-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-151">Events \subseteq Influences</script> of events, partitioned
- into disjoint subsets <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-152-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">,</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi><mo stretchy="false">,</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">,</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-152">Starts, Ends, Generations, Usages,
+<ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-159-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-159">Events \subseteq Influences</script> of events, partitioned
+ into disjoint subsets <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-160-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">,</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi><mo stretchy="false">,</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">,</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-160">Starts, Ends, Generations, Usages,
Invalidations</script>.
-</li><li> A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-153-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-153">time : Events \to Times</script>.
+</li><li> A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-161-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-161">time : Events \to Times</script>.
</li>
-<li> A quasi-ordering on events <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-154-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯⊂</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-154">\preceq \subset Events \times
-Events</script>. We write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-155-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">≺</mo><msup><mi>e</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-155">e \prec e'</script> when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-156-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">⪯</mo><msup><mi>e</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-156">e \preceq e'</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-157-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">⪯̸</mo><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-157">e'
+<li> A quasi-ordering on events <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-162-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯⊂</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-162">\preceq \subset Events \times
+Events</script>. We write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-163-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">≺</mo><msup><mi>e</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-163">e \prec e'</script> when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-164-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">⪯</mo><msup><mi>e</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-164">e \preceq e'</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-165-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">⪯̸</mo><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-165">e'
\not\preceq e</script> hold.
</li>
-<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-158-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-158">started : Starts \to Activities \times Entities \times
-Activities</script>, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-159-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-159">started(st) = (a,e,a')</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-160-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-160">start \in
+<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-166-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-166">started : Starts \to Activities \times Entities \times
+Activities</script>, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-167-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-167">started(start) = (a,e,a')</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-168-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-168">start \in
events(a) \cap events(e) \cap events(a')</script>.
</li>
-<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-161-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-161">ended : Ends \to Activities \times Entities \times Activities</script>, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-162-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-162">ended(end) = (a,e,a')</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-163-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-163">end \in
+<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-169-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-169">ended : Ends \to Activities \times Entities \times Activities</script>, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-170-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-170">ended(end) = (a,e,a')</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-171-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-171">end \in
events(a) \cap events(e) \cap events(a')</script>.
</li>
-<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-164-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-164">used : Usages \to Activities \times Entities</script> such
-that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-165-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-165">used(use) = (a,e)</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-166-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-166">use \in
+<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-172-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-172">used : Usages \to Activities \times Entities</script> such
+that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-173-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-173">used(use) = (a,e)</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-174-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-174">use \in
events(a) \cap events(e)</script>.
</li>
-<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-167-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-167">generated : Generations \to Entities \times
-Activities</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-168-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-168">generated(gen) = (a,e)</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-169-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-169">gen \in
+<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-175-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-175">generated : Generations \to Entities \times
+Activities</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-176-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-176">generated(gen) = (a,e)</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-177-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-177">gen \in
events(a) \cap events(e)</script>.
</li>
-<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-170-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-170">invalidated : Invalidations \to Entities \times
-Activities</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-171-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-171">invalidated(inv) = (a,e)</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-172-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-172">inv \in
+<li>A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-178-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-178">invalidated : Invalidations \to Entities \times
+Activities</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-179-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-179">invalidated(inv) = (a,e)</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-180-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∩</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-180">inv \in
events(a) \cap events(e)</script>.
</li>
</ol>
@@ -1583,12 +1618,12 @@
<h5><span class="secno">3.2.4.2 </span> Associations </h5>
-<p>An <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-173-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-173">Association</script> is an influence relating an agent to an activity
+<p>An <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-181-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-181">Association</script> is an influence relating an agent to an activity
and optional plan. To model associations, we introduce:
</p>
<div class="component" id="associations" data-count="10" data-title="Component 10 (associations)"><div class="ruleTitle"><a class="internalDFN" href="#associations">Component 10 (associations)</a></div>
- <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-174-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-174">Associations \subseteq Influences</script> with associated
- function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-175-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">:</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi mathvariant="normal">⊥</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-175">associatedWith : Associations \to Agents \times Activities \times Plans_\bot</script>.
+ <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-182-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-182">Associations \subseteq Influences</script> with associated
+ function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-183-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">:</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi mathvariant="normal">⊥</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-183">associatedWith : Associations \to Agents \times Activities \times Plans_\bot</script>.
</p>
</div>
</section>
@@ -1596,23 +1631,23 @@
<h5><span class="secno">3.2.4.3 </span> Attributions </h5>
-<p>An <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-176-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-176">Attribution</script> is an influence relating an entity to an agent. To model attributions, we introduce:
+<p>An <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-184-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-184">Attribution</script> is an influence relating an entity to an agent. To model attributions, we introduce:
</p>
<div class="component" id="attributions" data-count="11" data-title="Component 11 (attributions)"><div class="ruleTitle"><a class="internalDFN" href="#attributions">Component 11 (attributions)</a></div>
- <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-177-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-177">Attributions \subseteq Influences</script> with associated
- function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-178-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">:</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-178">attributedTo : Attributions \to Entities \times Agents</script>.
+ <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-185-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-185">Attributions \subseteq Influences</script> with associated
+ function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-186-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">:</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-186">attributedTo : Attributions \to Entities \times Agents</script>.
</p>
</div>
</section>
<section id="communications-1">
<h5><span class="secno">3.2.4.4 </span>Communications</h5>
- <p>A <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-179-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-179">Communication</script> is an influence indicating exchange of
+ <p>A <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-187-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-187">Communication</script> is an influence indicating exchange of
information between activities. To model communications, we introduce:
</p>
<div class="component" id="communications" data-count="12" data-title="Component 12 (communications)"><div class="ruleTitle"><a class="internalDFN" href="#communications">Component 12 (communications)</a></div>
- <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-180-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-180">Communications \subseteq Influences</script> with associated
- function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-181-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-181">communicated : Communications \to Activities \times Activities</script>.
+ <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-188-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-188">Communications \subseteq Influences</script> with associated
+ function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-189-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-189">communicated : Communications \to Activities \times Activities</script>.
</p>
</div>
@@ -1620,12 +1655,12 @@
</section>
<section id="delegations-1">
<h5><span class="secno">3.2.4.5 </span>Delegations</h5>
-<p>A <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-182-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-182">Delegation</script> is an influence relating two agents. To
+<p>A <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-190-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-190">Delegation</script> is an influence relating two agents. To
model delegations, we introduce:
</p>
<div class="component" id="delegations" data-count="13" data-title="Component 13 (delegations)"><div class="ruleTitle"><a class="internalDFN" href="#delegations">Component 13 (delegations)</a></div>
- <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-183-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-183">Delegations \subseteq Influences</script> and associated function
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-184-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">:</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-184">actedFor : Delegations \to Agents \times Agents \times Activities</script>
+ <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-191-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-191">Delegations \subseteq Influences</script> and associated function
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-192-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">:</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-192">actedFor : Delegations \to Agents \times Agents \times Activities</script>
</p>
</div>
@@ -1634,60 +1669,60 @@
<h5><span class="secno">3.2.4.6 </span> Derivations </h5>
-<p>A <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-185-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-185">Derivation</script> is an influence chaining one or more
+<p>A <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-193-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-193">Derivation</script> is an influence chaining one or more
generation and use steps. To model derivations, we introduce an
auxiliary notion of <em>derivation path</em>. These paths are of the form </p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-186-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo stretchy="false">−</mo><mn>1</mn></mrow></msub><mo stretchy="false">⋅</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>0</mn></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-186">ent_n\cdot g_n\cdot act_n\cdot u_n\cdot ent_{n-1}\cdot ...\cdot
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-194-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo stretchy="false">−</mo><mn>1</mn></mrow></msub><mo stretchy="false">⋅</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>0</mn></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-194">ent_n\cdot g_n\cdot act_n\cdot u_n\cdot ent_{n-1}\cdot ...\cdot
ent_1\cdot g_1\cdot act_1\cdot u_1\cdot ent_0</script>
-<p>where the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-187-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-187">ent_i</script> are entities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-188-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-188">act_i</script> are activities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-189-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-189">g_i</script> are generations, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-190-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-190">u_i</script> are usages.
+<p>where the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-195-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-195">ent_i</script> are entities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-196-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-196">act_i</script> are activities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-197-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-197">g_i</script> are generations, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-198-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-198">u_i</script> are usages.
</p>
<p>Formally, we consider the (regular) language:
</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-191-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mo stretchy="false">(</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msup><mo stretchy="false">)</mo><mo stretchy="false">+</mo></msup></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-191">DerivationPaths = Entities \cdot (Generations \cdot Activities \cdot
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-199-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mo stretchy="false">(</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msup><mo stretchy="false">)</mo><mo stretchy="false">+</mo></msup></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-199">DerivationPaths = Entities \cdot (Generations \cdot Activities \cdot
Usages \cdot Entities)^+</script>
<p>with the constraints that for each derivation path:
</p>
<ul>
-<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-192-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-192">ent\cdot g \cdot act</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-193-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-193">generated(g) = (ent,act)</script>, and
+<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-200-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-200">ent\cdot g \cdot act</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-201-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-201">generated(g) = (ent,act)</script>, and
</li>
-<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-194-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-194">act \cdot u \cdot ent</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-195-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-195">used(u) = (act,ent)</script>.
+<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-202-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-202">act \cdot u \cdot ent</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-203-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-203">used(u) = (act,ent)</script>.
</li>
</ul>
<div class="component" id="derivations" data-count="14" data-title="Component 14 (derivations)"><div class="ruleTitle"><a class="internalDFN" href="#derivations">Component 14 (derivations)</a></div>
-<p> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-196-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-196">Derivations \subseteq Influences</script> with an associated
- function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-197-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">:</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-197">derivationPath : Derivations \to
+<p> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-204-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-204">Derivations \subseteq Influences</script> with an associated
+ function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-205-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">:</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-205">derivationPath : Derivations \to
DerivationPaths</script> linking each derivation to a derivation path. </p>
<p></p>
</div>
<div class="remark">
<p>
- The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-198-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-198">derivationPath</script> function links each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-199-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-199"> d \in Derivations</script> to a
+ The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-206-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-206">derivationPath</script> function links each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-207-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-207"> d \in Derivations</script> to a
derivation path. A derivation has exactly one associated derivation
path. However, if the PROV-N statement <span class="name">wasDerivedFrom(e_2,e_1,-,-,-)</span> is asserted in an
- instance, there may be multiple derivation paths linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-200-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-200">e_2</script> to
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-201-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-201">e_1</script>, each corresponding to a different path, identified by different
- derivations <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-202-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-202">d \in Derivations</script>.
+ instance, there may be multiple derivation paths linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-208-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-208">e_2</script> to
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-209-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-209">e_1</script>, each corresponding to a different path, identified by different
+ derivations <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-210-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-210">d \in Derivations</script>.
</p>
<p>A derivation path implies the existence of at least one chained generation
and use step. However, not all such potential derivation paths are associated
with derivations; there can (and in general will) be many such paths
that are not associated with derivation steps. In other words, because we require derivations to be
- explicitly assocated with derivation paths, it is not sound to infer
+ explicitly associated with derivation paths, it is not sound to infer
the existence of a derivation from the existence of an
alternating generation/use chain.
</p>
<p>
The reason why we need paths and not just individual derivation
- steps is to reflect that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-203-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-203">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> formulas can
+ steps is to reflect that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-211-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-211">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> formulas can
represent multiple derivation steps. However, there is no way to
- express a multi-step derivation path in PROV: any valid PROV
- instance turns out to have a model in which all derivation paths are
+ force a derivation to take multiple steps. Any valid PROV
+ instance has a model in which all derivation paths are
one-step.</p></div>
</section>
@@ -1705,138 +1740,143 @@
<ol>
<li id="axiom1">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-204-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-204">generated(g) = (e,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-205-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-205">used(u) = (a_2,e)</script> then there
- exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-206-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-206">c \in Communications</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-207-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-207">communicated(c) = (a_2,a_1)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-212-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-212">generated(g) = (e,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-213-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-213">used(u) = (a_2,e)</script> then there
+ exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-214-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-214">c \in Communications</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-215-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-215">communicated(c) = (a_2,a_1)</script>.
</li>
<li id="axiom2">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-208-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-208">e \in Entities</script> then there exist <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-209-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-209">gen,inv,a,a'</script> such that
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-210-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-210">generated(gen) = (e,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-211-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-211">invalidated(inv) = (e,a')</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-216-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-216">e \in Entities</script> then there exist <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-217-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-217">gen,inv,a,a'</script> such that
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-218-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-218">generated(gen) = (e,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-219-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-219">invalidated(inv) = (e,a')</script>.
</li>
<li id="axiom3">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-212-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-212">started(start) = (a_2,e,a_1)</script> then there exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-213-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-213">gen</script> such
- that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-214-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-214">generated(gen) = (e,a_1)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-220-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-220">started(start) = (a_2,e,a_1)</script> then there exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-221-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-221">gen</script> such
+ that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-222-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-222">generated(gen) = (e,a_1)</script>.
</li>
<li id="axiom4">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-215-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-215">ended(end) = (a_2,e,a_1)</script> then there exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-216-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-216">gen</script> such
- that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-217-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-217">generated(gen) = (e,a_1)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-223-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-223">ended(end) = (a_2,e,a_1)</script> then there exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-224-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-224">gen</script> such
+ that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-225-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-225">generated(gen) = (e,a_1)</script>.
</li>
<li id="axiom5">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-218-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-218">d \in Derivations</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-219-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-219">prov:Revision \in
- value(d,prov:type)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-220-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-220">derivationPath(deriv) = e_2 \cdot w \cdot
- e_1</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-221-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-221">thingOf(e_1) = thingOf(e_2)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-226-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-226">d \in Derivations</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-227-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-227">prov:Revision \in
+ value(d,prov:type)</script> and there exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-228-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo stretchy="false">∈</mo><mo stretchy="false">(</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>U</mi><mi>s</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msup><mo stretchy="false">)</mo><mo stretchy="false">∗</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-228">w \in (Generations \cup
+ Activities \cup Uses \cup Entities)^* </script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-229-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-229">derivationPath(deriv) = e_2 \cdot w \cdot
+ e_1 \in DerivationPaths</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-230-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-230">thingOf(e_1) = thingOf(e_2)</script>.
</li>
<li id="axiom6">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-222-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-222">attributedTo(att) = (e,ag)</script> then there exist <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-223-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-223">gen</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-224-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-224">assoc</script>
- such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-225-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-225">generated(gen) = (e,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-226-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-226">associatedWith(assoc) = (a,ag)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-231-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-231">attributedTo(att) = (e,ag)</script> then there exist <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-232-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-232">gen</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-233-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-233">assoc</script>
+ and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-234-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-234">a</script>
+ such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-235-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-235">generated(gen) = (e,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-236-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-236">associatedWith(assoc) = (a,ag)</script>.
</li>
<li id="axiom7">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-227-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-227">actedFor(deleg) = (ag_2,ag_1,act)</script> then there exist
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-228-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-228">assoc_1,assoc_2,pl_1,pl_2</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-229-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-229">associatedWith(assoc_1) = (ag_1,act,pl_1)</script>
- and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-230-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-230">associatedWith(assoc_2) = (ag_2,act,pl_2)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-237-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-237">actedFor(deleg) = (ag_2,ag_1,act)</script> then there exist
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-238-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-238">assoc_1,assoc_2,pl_1,pl_2</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-239-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-239">associatedWith(assoc_1) = (ag_1,act,pl_1)</script>
+ and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-240-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-240">associatedWith(assoc_2) = (ag_2,act,pl_2)</script>.
</li>
<li id="axiom8">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-231-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-231">generated(id) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-232-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-232">influenced(id) = (e,a)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-241-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-241">generated(id) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-242-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-242">influenced(id) = (e,a)</script>.
</li>
<li id="axiom9">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-233-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-233">used(id) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-234-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-234">influenced(id) = (e,a)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-243-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-243">used(id) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-244-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-244">influenced(id) = (e,a)</script>.
</li>
<li id="axiom10">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-235-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-235">communicated(id) = (a_2,a_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-236-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-236">influenced(id) = (a_2,a_1)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-245-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-245">communicated(id) = (a_2,a_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-246-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-246">influenced(id) = (a_2,a_1)</script>.
</li>
<li id="axiom11">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-237-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-237">started(id) = (a_2,e,a_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-238-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-238">influenced(id) = (a_2,e)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-247-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-247">started(id) = (a_2,e,a_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-248-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-248">influenced(id) = (a_2,e)</script>.
</li>
<li id="axiom12">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-239-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-239">ended(id) = (a_2,e,a_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-240-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-240">influenced(id) = (a_2,e)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-249-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-249">ended(id) = (a_2,e,a_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-250-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-250">influenced(id) = (a_2,e)</script>.
</li>
<li id="axiom13">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-241-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-241">invalidated(id) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-242-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-242">influenced(id) = (e,a)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-251-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-251">invalidated(id) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-252-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-252">influenced(id) = (e,a)</script>.
</li>
<li id="axiom14">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-243-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-243">derivationPath(id) = e_2 \cdot w \cdot e_1</script> then
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-244-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-244">influenced(id) = (e_2,e_1)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-253-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-253">derivationPath(id) = e_2 \cdot w \cdot e_1</script> then
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-254-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-254">influenced(id) = (e_2,e_1)</script>.
</li>
<li id="axiom15">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-245-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-245">attributedTo(id) = (e,ag)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-246-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-246">influenced(id) = (e,ag)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-255-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-255">attributedTo(id) = (e,ag)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-256-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-256">influenced(id) = (e,ag)</script>.
</li>
<li id="axiom16">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-247-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-247">associatedWith(id) = (a,ag,pl)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-248-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-248">influenced(id) = (a,ag)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-257-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-257">associatedWith(id) = (a,ag,pl)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-258-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-258">influenced(id) = (a,ag)</script>.
</li>
<li id="axiom17">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-249-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-249">actedFor(id) = (ag_2,ag_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-250-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-250">influenced(id) = (ag_2,ag_1)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-259-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-259">actedFor(id) = (ag_2,ag_1)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-260-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-260">influenced(id) = (ag_2,ag_1)</script>.
</li>
<li id="axiom18">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-251-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msup><mi>n</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-251">generated(gen) = (e,a) = generated(gen')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-252-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msup><mi>n</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-252">gen = gen'</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-261-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msup><mi>n</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-261">generated(gen) = (e,a) = generated(gen')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-262-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msup><mi>n</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-262">gen = gen'</script>.
</li>
<li id="axiom19">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-253-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msup><mi>v</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-253">invalidated(inv) = (e,a) = invalidated(inv')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-254-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msup><mi>v</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-254">inv=inv'</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-263-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msup><mi>v</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-263">invalidated(inv) = (e,a) = invalidated(inv')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-264-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msup><mi>v</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-264">inv=inv'</script>.
</li>
<li id="axiom20">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-255-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-255">started(st) = (a,e_1,a')</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-256-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-256">started(st') = (a,e_2,a')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-257-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mo stretchy="false">=</mo><mi>s</mi><msup><mi>t</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-257">st=st'</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-265-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-265">started(st) = (a,e_1,a')</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-266-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-266">started(st') = (a,e_2,a')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-267-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mo stretchy="false">=</mo><mi>s</mi><msup><mi>t</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-267">st=st'</script>.
</li>
<li id="axiom21">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-258-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-258">ended(end) = (a,e_1,a')</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-259-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msup><mi>d</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-259">ended(end') = (a,e_2,a')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-260-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msup><mi>d</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-260">end=end'</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-268-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-268">ended(end) = (a,e_1,a')</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-269-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msup><mi>d</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-269">ended(end') = (a,e_2,a')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-270-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msup><mi>d</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-270">end=end'</script>.
</li>
<li id="axiom22">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-261-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-261">started(st) = (a,e)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-262-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-262">st \preceq evt</script> for all <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-263-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">−</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-263">evt \in
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-271-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-271">started(st) = (a,e,a')</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-272-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-272">st \preceq evt</script> for all <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-273-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">−</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-273">evt \in
events(a) - Invalidations</script>.
</li>
<li id="axiom23">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-264-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-264">ended(end) = (a,e,a') </script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-265-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-265">evt \preceq end</script> for all
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-266-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">−</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-266">evt \in events(a) - Invalidations</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-274-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-274">ended(end) = (a,e,a') </script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-275-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-275">evt \preceq end</script> for all
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-276-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">−</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-276">evt \in events(a) - Invalidations</script>.
</li>
<li id="axiom24">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-267-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-267">generated(gen) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-268-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-268">gen \preceq evt</script> for all <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-269-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-269">evt \in events(e)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-277-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-277">generated(gen) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-278-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-278">gen \preceq evt</script> for all <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-279-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-279">evt \in events(e)</script>.
</li>
<li id="axiom25">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-270-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-270">invalidated(inv) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-271-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-271">evt\preceq inv</script> for all
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-272-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-272">evt \in events(e)</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-280-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-280">invalidated(inv) = (e,a)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-281-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-281">evt\preceq inv</script> for all
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-282-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-282">evt \in events(e)</script>.
</li>
<li id="axiom26">
- For any derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-273-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-273">deriv</script>, with path <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-274-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-274">derivationPath(deriv) = w</script>,
- if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-275-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-275">e_2 \cdot g \cdot a \cdot u \cdot e_1 </script> is a substring of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-276-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-276">w</script>
- where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-277-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-277">e_1,e_2 \in Entities</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-278-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-278">g \in Generations</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-279-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-279">u \in Usages</script>
- and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-280-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-280">a \in Activities</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-281-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo stretchy="false">⪯</mo><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-281">u \preceq g</script>.
+ For any derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-283-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-283">deriv</script>, with path <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-284-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-284">derivationPath(deriv) = w</script>,
+ if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-285-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-285">e_2 \cdot g \cdot a \cdot u \cdot e_1 </script> is a substring of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-286-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-286">w</script>
+ where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-287-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-287">e_1,e_2 \in Entities</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-288-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-288">g \in Generations</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-289-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-289">u \in Usages</script>
+ and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-290-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-290">a \in Activities</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-291-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo stretchy="false">⪯</mo><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-291">u \preceq g</script>.
</li>
<li id="axiom27">
- For any derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-282-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-282">deriv</script>, with path <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-283-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-283">derivationPath(deriv) = e_2
- \cdot w \cdot e_1</script>, if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-284-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-284">generated(gen_1) = (e_1,a_1)</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-285-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-285">generated(gen_2) = (e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-286-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">≺</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-286">gen_1 \prec gen_2</script>.
+ For any derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-292-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-292">deriv</script>, with path <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-293-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-293">derivationPath(deriv) = e_2
+ \cdot w \cdot e_1</script>, if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-294-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-294">generated(gen_1) = (e_1,a_1)</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-295-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-295">generated(gen_2) = (e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-296-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">≺</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-296">gen_1 \prec gen_2</script>.
</li>
<li id="axiom28">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-287-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-287">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-288-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-288">started(start) = (a,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-289-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-289">invalidated(inv) =
- (ag,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-290-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-290">start \preceq inv</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-297-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-297">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-298-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-298">started(start) = (a,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-299-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-299">invalidated(inv) =
+ (ag,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-300-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-300">start \preceq inv</script>.
</li>
<li id="axiom29">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-291-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-291">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-292-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-292">generated(gen) =
- (ag,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-293-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-293">ended(end) = (a,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-294-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-294">gen \preceq end</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-301-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-301">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-302-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-302">generated(gen) =
+ (ag,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-303-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-303">ended(end) = (a,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-304-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-304">gen \preceq end</script>.
</li>
<li id="axiom30">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-295-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-295">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-296-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-296">started(start) = (a,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-297-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-297">ended(end) =
- (ag,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-298-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-298">start \preceq end</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-305-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-305">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-306-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-306">started(start) = (a,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-307-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-307">ended(end) =
+ (ag,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-308-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-308">start \preceq end</script>.
</li>
<li id="axiom31">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-299-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-299">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-300-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-300">started(start) =
- (ag,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-301-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-301">ended(end) = (a,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-302-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-302">start \preceq end</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-309-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-309">associatedWith(assoc) = (a,ag,pl)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-310-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-310">started(start) =
+ (ag,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-311-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-311">ended(end) = (a,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-312-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-312">start \preceq end</script>.
</li>
<li id="axiom32">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-303-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-303">attributedTo(attrib) = (e,ag)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-304-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-304">generated(gen_1) =
- (ag_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-305-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-305">generated(gen_2) = (e,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-306-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-306">gen_1 \preceq gen_2</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-313-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-313">attributedTo(attrib) = (e,ag)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-314-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-314">generated(gen_1) =
+ (ag_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-315-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-315">generated(gen_2) = (e,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-316-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-316">gen_1 \preceq gen_2</script>.
</li>
<li id="axiom33">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-307-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-307">attributedTo(attrib) = (e,ag)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-308-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-308">started(start) =
- (ag_1,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-309-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-309">generated(gen) = (e,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-310-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-310">start \preceq gen</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-317-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-317">attributedTo(attrib) = (e,ag)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-318-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-318">started(start) =
+ (ag_1,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-319-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-319">generated(gen) = (e,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-320-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-320">start \preceq gen</script>.
</li>
<li id="axiom34">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-311-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-311">actedFor(deleg) = (ag_2,ag_1,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-312-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-312">generated(gen) =
- (ag_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-313-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-313">invalidated(inv) = (ag_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-314-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-314">gen \preceq inv</script>.
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-321-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-321">actedFor(deleg) = (ag_2,ag_1,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-322-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-322">generated(gen) =
+ (ag_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-323-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-323">invalidated(inv) = (ag_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-324-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-324">gen \preceq inv</script>.
</li>
<li id="axiom35">
- If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-315-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-315">actedFor(deleg) = (ag_2,ag_1,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-316-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-316">started(start) =
- (ag_1,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-317-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-317">ended(end) = (ag_2,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-318-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-318">start \preceq
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-325-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-325">actedFor(deleg) = (ag_2,ag_1,a)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-326-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-326">started(start) =
+ (ag_1,e_1,a_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-327-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-327">ended(end) = (ag_2,e_2,a_2)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-328-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-328">start \preceq
end</script>.
</li>
- </ol>
+ <li id="axiom36">
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-329-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-329">e \in Entity</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-330-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-330">prov:emptyCollection \in
+ value(e,prov:type)</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-331-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-331">e \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-332-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-332">members(e) = \emptyset</script>.
+ </li></ol>
</div>
<p>These properties are called <em>axioms</em>, and they are
@@ -1852,17 +1892,21 @@
should be a constraint analogous to Constraint 34 that specifies
that any invalidation event in which an activity participates must
follow the activity's start event(s) and precede its end
- event(s).</p>
+ event(s).
+ </p>
+ <p>Here, we exempt invalidations from axioms 22 and 23 in order to
+ simplify the proof of weak completeness.</p>
+
</div>
</section>
<section id="putting-it-all-together">
<h3><span class="secno">3.4 </span> Putting it all together </h3>
-<p>A <em>PROV structure</em> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-319-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-319">W</script> is a collection of sets, functions, and relations containing all of the above
+<p>A <em>PROV structure</em> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-333-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-333">W</script> is a collection of sets, functions, and relations containing all of the above
described components and satisfying all of the associated properties
-and axions. If we need to talk about the objects or relations of
-more than one structure then we may write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-320-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-320">W_1.Objects</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-321-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-321">W_1.Things</script>,
+and axioms. If we need to talk about the objects or relations of
+more than one structure then we may write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-334-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-334">W_1.Objects</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-335-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-335">W_1.Things</script>,
etc.; otherwise, to
decrease notational clutter, when we consider a fixed structure then the names of the sets, relations and functions above refer to the components of that model.
</p>
@@ -1871,9 +1915,9 @@
<p>
Some features of PROV structures are relatively obvious or routine,
corresponding directly to features of PROV and associated inferences.
-For example, the functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-322-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-322">used, generated, invalidated, started,
+For example, the functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-336-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-336">used, generated, invalidated, started,
ended</script> mapping events to their associated entities or activities, and
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-323-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-323">communicated, associatedWith, attributedTo, actedFor</script> associating
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-337-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-337">communicated, associatedWith, attributedTo, actedFor</script> associating
other types of influences with appropriate data.
</p>
<p>
@@ -1883,11 +1927,11 @@
paths are one such distinctive feature; they correspond to an
intuition that derivations may describe one or multiple generation-use
steps leading from one entity to another. Another distinctive feature
-is the use of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-324-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-324">Things</script>, which correspond to changing, real-world
-things, as opposed to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-325-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-325">Entities</script>, which correspond to limited views or
-perspectives on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-326-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-326">Things</script>, with some fixed aspects. The semantic
-structures of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-327-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-327">Things</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-328-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-328">Entities</script> provides a foundation for the
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-329-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-329">alternateOf</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-330-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-330">specializationOf</script> relations.
+is the use of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-338-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-338">Things</script>, which correspond to changing, real-world
+things, as opposed to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-339-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-339">Entities</script>, which correspond to limited views or
+perspectives on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-340-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-340">Things</script>, with some fixed aspects. The semantic
+structures of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-341-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-341">Things</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-342-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-342">Entities</script> provide a foundation for the
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-343-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-343">alternateOf</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-344-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-344">specializationOf</script> relations.
</p>
@@ -1897,10 +1941,10 @@
<h3><span class="secno">3.5 </span> Interpretations </h3>
<p>We need to link identifiers to the objects they denote. We do this using a function which we shall call an <em>interpretation</em>.
- An interpretation is a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-331-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">:</mo><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">→</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-331">\rho : Identifiers \to Objects</script> describing
+ An interpretation is a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-345-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">:</mo><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">→</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-345">\rho : Identifiers \to Objects</script> describing
which object is the target of each identifier. The mapping from
identifiers to objects may <b>not</b> change over time; only
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-332-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-332">Objects</script> can be denoted by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-333-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-333">Identifiers</script>.
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-346-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-346">Objects</script> can be denoted by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-347-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-347">Identifiers</script>.
</p>
</section>
@@ -1909,59 +1953,59 @@
<section id="semantics">
<!--OddPage--><h2><span class="secno">4. </span> Semantics </h2>
-<p>In what follows, let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-334-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-334">W</script> be a fixed structure with the associated sets and relations discussed in the previous section, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-335-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-335">\rho</script> be an interpretation of identifiers as objects in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-336-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-336">W</script>.
+<p>In what follows, let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-348-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-348">W</script> be a fixed structure with the associated sets and relations discussed in the previous section, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-349-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-349">\rho</script> be an interpretation of identifiers as objects in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-350-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-350">W</script>.
The annotations [WF] refer to well-formedness constraints that correspond to typing constraints.
</p>
<section id="satisfaction">
<h3><span class="secno">4.1 </span> Satisfaction </h3>
-<p>Consider a formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-337-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-337">\phi</script>, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-338-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-338">W</script> and an interpretation
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-339-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-339">\rho</script>.
-We define notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-340-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-340">W,\rho \models \phi</script> which means that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-341-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-341">\phi</script> is
- satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-342-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-342">W,\rho</script>. For atomic formulas, the definition of the
+<p>Consider a formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-351-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-351">\phi</script>, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-352-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-352">W</script> and an interpretation
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-353-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-353">\rho</script>.
+We define notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-354-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-354">W,\rho \models \phi</script> which means that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-355-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-355">\phi</script> is
+ satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-356-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-356">W,\rho</script>. For atomic formulas, the definition of the
satisfaction relation is given in the next few subsections. We give
the standard definition of the semantics of the other formulas:
</p>
<div class="semantics" id="first-order-logic-semantics" data-count="16" data-title="Semantics 16 (first-order-logic-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#first-order-logic-semantics">Semantics 16 (first-order-logic-semantics)</a></div>
<ol>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-343-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-343">W,\rho \models True</script> always holds.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-344-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-344">W,\rho \models False</script> never holds.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-345-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">=</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-345">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-346-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-346">\rho(x) =
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-357-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-357">W,\rho \models True</script> always holds.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-358-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-358">W,\rho \models False</script> never holds.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-359-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">=</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-359">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-360-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-360">\rho(x) =
\rho(y)</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-347-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">¬</mi><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-347">W,\rho \models \neg \phi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-348-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-348">W,\rho \models
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-361-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">¬</mi><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-361">W,\rho \models \neg \phi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-362-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-362">W,\rho \models
\phi</script> does not hold.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-349-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∧</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-349">W,\rho \models \phi \wedge \psi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-350-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-350">W,\rho \models
- \phi</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-351-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-351">W,\rho \models \psi</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-352-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-352">W,\rho \models \phi \vee \psi</script> holds if either <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-353-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-353">W,\rho \models \phi</script>
- or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-354-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-354">W,\rho \models \psi</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-355-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">⇒</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-355">W,\rho \models \phi \Rightarrow \psi</script> holds if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-356-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-356">W,\rho \models \phi</script>
- implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-357-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-357">W,\rho \models \psi</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-358-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-358">W,\rho \models \exists x. \phi</script> holds if there exists some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-359-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-359">obj \in
- Objects</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-360-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-360">W,\rho[x:=obj] \models \phi</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-361-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-361">W,\rho \models \forall x. \phi</script> holds if there for every <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-362-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-362">obj \in
- Objects</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-363-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-363">W,\rho[x:=obj] \models \phi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-363-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∧</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-363">W,\rho \models \phi \wedge \psi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-364-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-364">W,\rho \models
+ \phi</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-365-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-365">W,\rho \models \psi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-366-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-366">W,\rho \models \phi \vee \psi</script> holds if either <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-367-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-367">W,\rho \models \phi</script>
+ or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-368-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-368">W,\rho \models \psi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-369-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">⇒</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-369">W,\rho \models \phi \Rightarrow \psi</script> holds if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-370-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-370">W,\rho \models \phi</script>
+ implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-371-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-371">W,\rho \models \psi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-372-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-372">W,\rho \models \exists x. \phi</script> holds if there exists some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-373-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-373">obj \in
+ Objects</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-374-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-374">W,\rho[x:=obj] \models \phi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-375-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-375">W,\rho \models \forall x. \phi</script> holds if there for every <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-376-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-376">obj \in
+ Objects</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-377-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-377">W,\rho[x:=obj] \models \phi</script>.</li>
</ol></div>
<div class="remark">
<p>In the semantics above, note that the domain of quantification is
- the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-364-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-364">Objects</script>; that is, quantifiers range over entities,
+ the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-378-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-378">Objects</script>; that is, quantifiers range over entities,
activities, agents, or influences (which are in turn further
- subdivided into types of influences). <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-365-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-365">Things</script> and relations
+ subdivided into types of influences). <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-379-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-379">Things</script> and relations
cannot be referenced directly by identifiers.
</p>
</div>
<div class="remark">
- <p>A PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-366-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-366">I</script> consists of a set of statements, each of
+ <p>A PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-380-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-380">I</script> consists of a set of statements, each of
which can be translated to an atomic formula following the
definitional rules in PROV-CONSTRAINTS, possibly by introducing
fresh existential variables. Thus, we can view an
- instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-367-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-367">I</script> as a set of atomic formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-368-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-368">\{\phi_1,\ldots,\phi_n\}</script>, or equivalently a
- single formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-369-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∃</mi><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo>.</mo><mtext> </mtext><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-369">\exists x_1,\ldots,x_k.~\phi_1 \wedge \cdots
- \wedge \phi_n</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-370-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-370">x_1,\ldots,x_k</script> are the existential
- variables of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-371-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-371">I</script>.
+ instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-381-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-381">I</script> as a set of atomic formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-382-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-382">\{\phi_1,\ldots,\phi_n\}</script>, or equivalently a
+ single formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-383-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∃</mi><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo>.</mo><mtext> </mtext><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-383">\exists x_1,\ldots,x_k.~\phi_1 \wedge \cdots
+ \wedge \phi_n</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-384-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-384">x_1,\ldots,x_k</script> are the existential
+ variables of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-385-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-385">I</script>.
</p>
</div>
@@ -1971,9 +2015,9 @@
<h3><span class="secno">4.2 </span> Attribute matching </h3>
-<p>We say that an object <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-372-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-372">obj</script> matches attributes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-373-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>v</mi><mi>a</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">]</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-373">[attr_1=val_1,...]</script> in structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-374-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-374">W</script> provided:
-for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-375-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-375">attr_i</script>, we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-376-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><msub><mi>l</mi><mi>i</mi></msub><mo stretchy="false">∈</mo><mi>W</mi><mo>.</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-376">val_i \in W.value(obj,attr_i)</script>.
-This is sometimes abbreviated as: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-377-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-377">match(W,obj,attrs)</script>.
+<p>We say that an object <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-386-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-386">obj</script> matches attributes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-387-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>v</mi><mi>a</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">]</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-387">[attr_1=val_1,...]</script> in structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-388-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-388">W</script> provided:
+for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-389-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-389">attr_i</script>, we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-390-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><msub><mi>l</mi><mi>i</mi></msub><mo stretchy="false">∈</mo><mi>W</mi><mo>.</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-390">val_i \in W.value(obj,attr_i)</script>.
+This is sometimes abbreviated as: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-391-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-391">match(W,obj,attrs)</script>.
</p>
</section>
@@ -1985,16 +2029,16 @@
<h4><span class="secno">4.3.1 </span> Entity </h4>
-<p>An entity formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-378-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-378">entity(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-379-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-379">id</script> denotes an entity.
+<p>An entity formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-392-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-392">entity(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-393-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-393">id</script> denotes an entity.
</p>
-<p>Entity formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-380-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-380">entity(id,attrs)</script> can be interpreted as follows:
+<p>Entity formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-394-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-394">entity(id,attrs)</script> can be interpreted as follows:
</p>
<div class="semantics" id="entity-semantics" data-count="17" data-title="Semantics 17 (entity-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#entity-semantics">Semantics 17 (entity-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-381-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-381">W,\rho \models entity(id,attrs)</script> holds if and only if:</p>
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-395-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-395">W,\rho \models entity(id,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-382-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-382">id</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-383-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-383">ent = \rho(id) \in Entities</script>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-396-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-396">id</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-397-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-397">ent = \rho(id) \in Entities</script>.
</li>
-<li>the attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-384-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-384">match(W,ent, attrs)</script>.
+<li>the attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-398-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-398">match(W,ent, attrs)</script>.
</li>
</ol>
@@ -2002,7 +2046,7 @@
</div>
<div class="remark">
<p>Not all of the attributes of an entity object are
- required to be present in an entity formula about that object. For example, the following formulas all hold if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-385-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-385">x</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-386-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-386">e</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-387-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>4</mn><mo stretchy="false">,</mo><mn>5</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">,</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-387">value(e,a) = \{4,5\}, value(e,b) = \{6\}</script> hold:
+ required to be present in an entity formula about that object. For example, the following formulas all hold if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-399-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-399">x</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-400-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-400">e</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-401-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>4</mn><mo stretchy="false">,</mo><mn>5</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">,</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-401">value(e,a) = \{4,5\}, value(e,b) = \{6\}</script> hold:
</p><pre> entity(x,[])
entity(x,[a=5])
entity(x,[a=4,a=5])
@@ -2020,42 +2064,52 @@
<h4><span class="secno">4.3.2 </span> Activity </h4>
-<p>An activity formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-388-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-388">activity(id,st,et,attrs)</script>
-where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-389-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-389">id</script> is a identifier referring to the activity, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-390-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-390">st</script> is a start
-time and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-391-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-391">et</script> is an end time, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-392-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-392">attrs</script> are the attributes of
-activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-393-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-393">id</script>.
+<p>An activity formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-402-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-402">activity(id,st,et,attrs)</script>
+where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-403-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-403">id</script> is a identifier referring to the activity, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-404-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-404">st</script> is a start
+time and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-405-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-405">et</script> is an end time, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-406-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-406">attrs</script> are the attributes of
+activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-407-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-407">id</script>.
</p>
<div class="semantics" id="activity-semantics" data-count="18" data-title="Semantics 18 (activity-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#activity-semantics">Semantics 18 (activity-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-394-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-394">W,\rho \models activity(id,st,et,attrs)</script>
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-408-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-408">W,\rho \models activity(id,st,et,attrs)</script>
holds if and only if:</p>
<ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-395-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-395">id</script> maps to an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-396-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-396">act = \rho(id) \in Activities</script>
-</li>
-<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-397-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-397">\rho(st) \in Times</script> is the activity's start time, that is:
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-398-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-398">startTime(id) = \rho(st)</script>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-409-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-409">id</script> maps to an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-410-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-410">act = \rho(id) \in Activities</script>.
</li>
-<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-399-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-399">\rho(et)</script> is the activity's end time, that is: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-400-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-400">endTime(id) = \rho(et)</script>
+<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-411-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-411">\rho(st) \in Times</script> is the activity's start time, that is:
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-412-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-412">startTime(act) = \rho(st)</script>.
</li>
-<li>There exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-401-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-401">start,e,a</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-402-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-402">started(start) = (act,e,a)</script>.</li>
-<li>There exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-403-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-403">end,e',a'</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-404-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-404">ended(end) = (act,e',a')</script>.</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-405-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-405">match(W,act,attrs)</script>.
+<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-413-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-413">\rho(et)</script> is the activity's end time, that is: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-414-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-414">endTime(act) = \rho(et)</script>.
+</li>
+<li>There exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-415-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-415">start,e,a</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-416-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-416">started(start) = (act,e,a)</script>,
+and for all such start events $startTime(act) = time(start).</li>
+<li>There exists <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-417-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-417">end,e',a'</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-418-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-418">ended(end) = (act,e',a')</script>, and
+for all such end events <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-419-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-419">endTime(act) = time(end)</script>.</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-420-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-420">match(W,act,attrs)</script>.
</li>
</ol>
</div>
+
+<div class="remark">
+ <p>The above definition is complicated for two reasons. First, we
+ need to ensure that every activity has a start and end event.
+ Second, when an <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-421-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-421">activity</script> formula is asserted, we need to make sure
+ all of the associated start and end event times match.
+ </p>
+ </div>
</section>
<section id="agent">
<h4><span class="secno">4.3.3 </span> Agent </h4>
-<p>An agent formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-406-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-406">agent(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-407-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-407">id</script> denotes the agent and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-408-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-408">attrs</script> describes additional attributes.
+<p>An agent formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-422-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-422">agent(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-423-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-423">id</script> denotes the agent and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-424-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-424">attrs</script> describes additional attributes.
</p>
<div class="semantics" id="agent-semantics" data-count="19" data-title="Semantics 19 (agent-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#agent-semantics">Semantics 19 (agent-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-409-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-409">W,\rho \models agent(id,attrs)</script> holds if and only if:
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-425-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-425">W,\rho \models agent(id,attrs)</script> holds if and only if:
</p>
<ol>
- <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-410-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-410">id</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-411-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-411">ag = \rho(id) \in Agents</script>
+ <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-426-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-426">id</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-427-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-427">ag = \rho(id) \in Agents</script>.
</li>
- <li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-412-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-412">match(W,ag,attrs)</script>.
+ <li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-428-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-428">match(W,ag,attrs)</script>.
</li>
</ol>
</div>
@@ -2070,25 +2124,25 @@
<h4><span class="secno">4.4.1 </span> Generation </h4>
<p>The generation formula is of the form
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-413-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-413">wasGeneratedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-414-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-414">id</script> is an event identifier,
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-415-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-415">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-416-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-416">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-417-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-417">attrs</script> is
-a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-418-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-418">t</script> is a time.
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-429-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-429">wasGeneratedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-430-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-430">id</script> is an event identifier,
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-431-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-431">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-432-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-432">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-433-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-433">attrs</script> is
+a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-434-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-434">t</script> is a time.
</p>
<div class="semantics" id="generation-semantics" data-count="20" data-title="Semantics 20 (generation-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#generation-semantics">Semantics 20 (generation-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-419-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-419">W,\rho \models
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-435-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-435">W,\rho \models
wasGeneratedBy(id,e,a,t,attrs)</script> holds if and only if:
</p><ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-420-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-420">id</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-421-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-421">evt = \rho(id) \in Generations</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-422-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-422">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-423-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-423">ent = \rho(e) \in Entities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-436-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-436">id</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-437-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-437">evt = \rho(id) \in Generations</script>.
</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-424-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-424">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-425-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-425">act = \rho(a) \in Activities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-438-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-438">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-439-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-439">ent = \rho(e) \in Entities</script>.
</li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-426-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-426">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-427-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-427">\rho(t) \in Times</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-428-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-428">time(evt) = \rho(t)</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-440-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-440">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-441-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-441">act = \rho(a) \in Activities</script>.
</li>
-<li>The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-429-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-429">act</script> generated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-430-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-430">ent</script> via <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-431-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-431">evt</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-432-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-432">generated(evt) = (ent,act)</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-442-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-442">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-443-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-443">\rho(t) \in Times</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-444-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-444">time(evt) = \rho(t)</script>.
</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-433-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-433">match(W,evt,attrs)</script>.
+<li>The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-445-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-445">act</script> generated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-446-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-446">ent</script> via <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-447-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-447">evt</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-448-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-448">generated(evt) = (ent,act)</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-449-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-449">match(W,evt,attrs)</script>.
</li>
</ol>
</div>
@@ -2097,49 +2151,49 @@
<section id="use">
<h4><span class="secno">4.4.2 </span> Use </h4>
-<p>The use formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-434-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-434">used(id,a,e,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-435-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-435">id</script>
-denotes an event, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-436-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-436">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-437-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-437">e</script> is an object
-identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-438-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-438">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-439-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-439">t</script> is a time.
+<p>The use formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-450-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-450">used(id,a,e,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-451-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-451">id</script>
+denotes an event, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-452-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-452">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-453-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-453">e</script> is an object
+identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-454-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-454">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-455-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-455">t</script> is a time.
</p>
<div class="semantics" id="usage-semantics" data-count="21" data-title="Semantics 21 (usage-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#usage-semantics">Semantics 21 (usage-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-440-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-440">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-456-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-456">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-441-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-441">id</script> denotes a usage event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-442-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-442">evt = \rho(id) \in Usages</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-443-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-443">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-444-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-444">act = \rho(id) \in Activities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-457-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-457">id</script> denotes a usage event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-458-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-458">evt = \rho(id) \in Usages</script>.
</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-445-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-445">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-446-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-446">ent = \rho(e) \in Entities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-459-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-459">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-460-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-460">act = \rho(id) \in Activities</script>.
</li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-447-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-447">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-448-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-448">\rho(t) \in Times</script>,
-i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-449-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-449">time(evt) = \rho(t)</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-461-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-461">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-462-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-462">ent = \rho(e) \in Entities</script>.
</li>
-<li>The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-450-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-450">act</script> used <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-451-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-451">obj</script> via <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-452-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-452">evt</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-453-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-453">used(evt) = (act,ent)</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-463-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-463">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-464-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-464">\rho(t) \in Times</script>,
+i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-465-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-465">time(evt) = \rho(t)</script>.
</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-454-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-454">match(W,evt,attrs)</script>.
+<li>The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-466-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-466">act</script> used <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-467-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-467">obj</script> via <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-468-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-468">evt</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-469-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-469">used(evt) = (act,ent)</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-470-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-470">match(W,evt,attrs)</script>.
</li></ol></div>
</section>
<section id="invalidation">
<h4><span class="secno">4.4.3 </span> Invalidation </h4>
-<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-455-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-455">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-456-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-456">id</script> is an event identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-457-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-457">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-458-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-458">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-459-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-459">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-460-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-460">t</script> is a time.</p>
-
-<div class="semantics" id="invalidation-semantics" data-count="22" data-title="Semantics 22 (invalidation-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-semantics">Semantics 22 (invalidation-semantics)</a></div> <p>An invalidation formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-461-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-461">W,\rho \models
+<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-471-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-471">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-472-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-472">id</script> is an event identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-473-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-473">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-474-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-474">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-475-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-475">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-476-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-476">t</script> is a time.</p>
+
+<div class="semantics" id="invalidation-semantics" data-count="22" data-title="Semantics 22 (invalidation-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-semantics">Semantics 22 (invalidation-semantics)</a></div> <p>An invalidation formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-477-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-477">W,\rho \models
wasInvalidatedBy(id,e,a,t,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-462-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-462">id</script> denotes an invalidation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-463-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-463">evt = \rho(id) \in Invalidations</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-464-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-464">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-465-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-465">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-466-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-466">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-467-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-467">act = \rho(a) \in Activities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-478-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-478">id</script> denotes an invalidation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-479-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-479">evt = \rho(id) \in Invalidations</script>.
</li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-468-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-468">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-469-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-469">\rho(t) \in Times</script>,
- i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-470-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-470">time(evt) = \rho(t)</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-480-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-480">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-481-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-481">ent = \rho(e) \in Entities</script>.
</li>
-<li>The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-471-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-471">act</script> invalidated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-472-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-472">ent</script> via <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-473-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-473">evt</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-474-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-474">invalidated(evt) = (ent,act)</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-482-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-482">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-483-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-483">act = \rho(a) \in Activities</script>.
</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-475-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-475">match(W,evt,attrs)</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-484-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-484">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-485-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-485">\rho(t) \in Times</script>,
+ i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-486-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-486">time(evt) = \rho(t)</script>.
+</li>
+<li>The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-487-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-487">act</script> invalidated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-488-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-488">ent</script> via <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-489-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-489">evt</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-490-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-490">invalidated(evt) = (ent,act)</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-491-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-491">match(W,evt,attrs)</script>.
</li></ol></div>
</section>
@@ -2147,81 +2201,81 @@
<h4><span class="secno">4.4.4 </span> Association </h4>
-<p>An association formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-476-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-476">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
+<p>An association formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-492-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-492">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
<div class="semantics" id="association-plan-semantics" data-count="23" data-title="Semantics 23 (association-plan-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#association-plan-semantics">Semantics 23 (association-plan-semantics)</a></div><p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-477-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-477">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-493-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-493">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-478-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-478">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-479-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-479">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-480-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-480">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-481-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-481">act = \rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-494-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-494">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-495-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-495">assoc = \rho(id) \in Associations</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-482-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-482">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-483-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-483">agent = \rho(ag) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-496-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-496">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-497-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-497">act = \rho(a) \in Activities</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-484-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-484">pl</script> denotes a plan <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-485-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-485">plan=\rho(pl) \in Plans</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-498-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-498">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-499-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-499">agent = \rho(ag) \in Agents</script>.
</li>
-<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-486-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-486">associatedWith(assoc) = (agent,act,plan)</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-500-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-500">pl</script> denotes a plan <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-501-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-501">plan=\rho(pl) \in Plans</script>.
</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-487-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-487">match(W,assoc,attrs)</script>.
+<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-502-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-502">associatedWith(assoc) = (agent,act,plan)</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-503-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-503">match(W,assoc,attrs)</script>.
</li></ol></div>
<div class="semantics" id="assocation-semantics" data-count="24" data-title="Semantics 24 (assocation-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#assocation-semantics">Semantics 24 (assocation-semantics)</a></div><p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-488-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-488">W,\rho \models wasAssociatedWith(id,a,ag,-,attrs)</script> holds if and only if:</p>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-504-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-504">W,\rho \models wasAssociatedWith(id,a,ag,-,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-489-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-489">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-490-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-490">assoc = \rho(id) \in Associations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-505-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-505">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-506-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-506">assoc = \rho(id) \in Associations</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-491-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-491">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-492-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-492">act = \rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-507-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-507">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-508-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-508">act = \rho(a) \in Activities</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-493-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-493">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-494-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-494">agent = \rho(ag) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-509-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-509">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-510-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-510">agent = \rho(ag) \in Agents</script>.
</li>
<li>The association associates the agent with the activity and no
- plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-495-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi mathvariant="normal">⊥</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-495">associatedWith(assoc) = (agent,act,\bot)</script>.
+ plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-511-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi mathvariant="normal">⊥</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-511">associatedWith(assoc) = (agent,act,\bot)</script>.
</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-496-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-496">match(W,assoc,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-512-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-512">match(W,assoc,attrs)</script>.
</li></ol></div>
</section>
<section id="start">
<h4><span class="secno">4.4.5 </span> Start </h4>
-<p>A start formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-497-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-497">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> is interpreted as follows:</p>
+<p>A start formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-513-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-513">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> is interpreted as follows:</p>
<div class="semantics" id="start-semantics" data-count="25" data-title="Semantics 25 (start-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#start-semantics">Semantics 25 (start-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-498-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-498">W,\rho \models wasStartedBy(id,a_2,e,a_1,t,attrs)</script> holds if and only if:</p>
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-514-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-514">W,\rho \models wasStartedBy(id,a_2,e,a_1,t,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-499-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-499">id</script> denotes a start event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-500-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-500">evt = \rho(id) \in Starts</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-501-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-501">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-502-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-502">act_2 = \rho(a_2) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-515-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-515">id</script> denotes a start event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-516-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-516">evt = \rho(id) \in Starts</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-503-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-503">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-504-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-504">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-505-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-505">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-506-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-506">act_1 = \rho(a_1) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-517-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-517">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-518-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-518">act_2 = \rho(a_2) \in Activities</script>.
</li>
-<li>The event happened at the start of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-507-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-507">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-508-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-508">\rho(t) = startTime(act_2) = time(evt)</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-519-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-519">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-520-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-520">ent = \rho(e) \in Entities</script>.
</li>
-<li> The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-509-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-509">act_1</script> started <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-510-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-510">act_2</script> via entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-511-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-511">ent</script>: that is,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-512-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-512">started(evt) = (act_2,ent,act_1)</script>.</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-513-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-513">match(W,evt,attrs)</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-521-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-521">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-522-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-522">act_1 = \rho(a_1) \in Activities</script>.
+</li>
+<li>The event happened at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-523-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-523">t</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-524-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">==</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-524">\rho(t) = = time(evt)</script>.
+</li>
+<li> The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-525-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-525">act_1</script> started <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-526-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-526">act_2</script> via entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-527-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-527">ent</script>: that is,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-528-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-528">started(evt) = (act_2,ent,act_1)</script>.</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-529-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-529">match(W,evt,attrs)</script>.
</li></ol></div>
</section>
<section id="end">
<h4><span class="secno">4.4.6 </span> End </h4>
-<p>An activity end formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-514-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-514">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> is interpreted as follows:</p>
+<p>An activity end formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-530-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-530">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> is interpreted as follows:</p>
<div class="semantics" id="end-semantics" data-count="26" data-title="Semantics 26 (end-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#end-semantics">Semantics 26 (end-semantics)</a></div>
<p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-515-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-515">W,\rho \models wasEndedBy(id,a_2,e,a_1,t,attrs)</script> holds if and only
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-531-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-531">W,\rho \models wasEndedBy(id,a_2,e,a_1,t,attrs)</script> holds if and only
if:</p>
<ol>
- <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-516-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-516">id</script> denotes an end event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-517-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-517">evt = \rho(id) \in Ends</script>.</li>
-<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-518-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-518">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-519-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-519">act_2 = \rho(a_2)\in Activities</script>.</li>
-<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-520-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-520">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-521-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-521">ent = \rho(e)\in Entities</script>.</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-522-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-522">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-523-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-523">act_1 = \rho(a_1)\in Activities</script>.</li>
-<li>The event happened at the end of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-524-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-524">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-525-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-525">\rho(t) = endTime(act_2) = time(evt)</script>.</li>
-<li> The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-526-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-526">act_1</script> ended <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-527-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-527">act_2</script> via entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-528-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-528">ent</script>: that is,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-529-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-529">ended(evt) = (act_2,ent,act_1)</script>.</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-530-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-530">match(W,evt,attrs)</script>.</li>
+ <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-532-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-532">id</script> denotes an end event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-533-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-533">evt = \rho(id) \in Ends</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-534-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-534">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-535-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-535">act_2 = \rho(a_2)\in Activities</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-536-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-536">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-537-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-537">ent = \rho(e)\in Entities</script>.</li>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-538-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-538">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-539-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-539">act_1 = \rho(a_1)\in Activities</script>.</li>
+<li>The event happened at the end of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-540-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-540">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-541-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-541">\rho(t) = endTime(act_2) = time(evt)</script>.</li>
+<li> The activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-542-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-542">act_1</script> ended <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-543-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-543">act_2</script> via entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-544-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-544">ent</script>: that is,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-545-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-545">ended(evt) = (act_2,ent,act_1)</script>.</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-546-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-546">match(W,evt,attrs)</script>.</li>
</ol>
</div>
</section>
@@ -2230,24 +2284,24 @@
<h4><span class="secno">4.4.7 </span> Attribution </h4>
<p>
-An attribution formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-531-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-531">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
+An attribution formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-547-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-547">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
</p>
<div class="semantics" id="attribution-semantics" data-count="27" data-title="Semantics 27 (attribution-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#attribution-semantics">Semantics 27 (attribution-semantics)</a></div>
<p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-532-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-532">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-548-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-548">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
holds if and only if:
</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-533-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-533">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-534-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-534">assoc = \rho(id) \in Associations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-549-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-549">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-550-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-550">assoc = \rho(id) \in Associations</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-535-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-535">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-536-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-536">ent = \rho(e) \in Entities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-551-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-551">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-552-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-552">ent = \rho(e) \in Entities</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-537-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-537">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-538-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-538">agent = \rho(ag) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-553-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-553">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-554-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-554">agent = \rho(ag) \in Agents</script>.
</li>
-<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-539-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-539">attributedTo(assoc)
+<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-555-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-555">attributedTo(assoc)
= (ent,agent)</script>.
</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-540-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-540">match(W,assoc,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-556-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-556">match(W,assoc,attrs)</script>.
</li></ol>
</div>
</section>
@@ -2255,23 +2309,23 @@
<section id="communication">
<h4><span class="secno">4.4.8 </span>Communication</h4>
-<p>A communication formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-541-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-541">wasInformedBy(id,a_2,a_2,attrs)</script> is
+<p>A communication formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-557-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-557">wasInformedBy(id,a_2,a_2,attrs)</script> is
interpreted as follows: </p>
<div class="semantics" id="communication-semantics" data-count="28" data-title="Semantics 28 (communication-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#communication-semantics">Semantics 28 (communication-semantics)</a></div>
<p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-542-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-542">W,\rho \models wasInformedBy(id,a_2,a_1,attrs)</script>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-558-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-558">W,\rho \models wasInformedBy(id,a_2,a_1,attrs)</script>
holds if and only if:
</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-543-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-543">id</script> denotes a communication <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-544-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-544">comm = \rho(id) \in Communications</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-559-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-559">id</script> denotes a communication <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-560-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-560">comm = \rho(id) \in Communications</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-545-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-545">a_1,a_2</script> denote activities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-546-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-546">act_1 = \rho(a_1) \in
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-561-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-561">a_1,a_2</script> denote activities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-562-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-562">act_1 = \rho(a_1) \in
Activities, act_2 = \rho(a_2)\in Activities</script>.
</li>
-<li>There exist <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-547-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-547">gen,use,ent</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-548-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-548">communicated(comm) =
-(act_2,act_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-549-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-549">generated(gen) = (ent,act_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-550-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-550">used(use) = (act_2,ent)</script>.
+<li>There exist <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-563-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-563">gen,use,ent</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-564-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-564">communicated(comm) =
+(act_2,act_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-565-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-565">generated(gen) = (ent,act_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-566-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-566">used(use) = (act_2,ent)</script>.
</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-551-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-551">match(W,comm,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-567-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-567">match(W,comm,attrs)</script>.
</li></ol>
</div>
</section>
@@ -2281,22 +2335,22 @@
<h4><span class="secno">4.4.9 </span> Delegation </h4>
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-552-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-552">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted using the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-553-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-553">ActsFor</script> relation as follows:</p>
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-568-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-568">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted as follows:</p>
<div class="semantics" id="delegation-semantics" data-count="29" data-title="Semantics 29 (delegation-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#delegation-semantics">Semantics 29 (delegation-semantics)</a></div>
<p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-554-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-554">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> holds if and only if:</p>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-569-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-569">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-555-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-555">id</script> denotes a delegation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-556-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-556">deleg=\rho(id) \in Delegations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-557-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-557">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-558-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-558">act=\rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-570-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-570">id</script> denotes a delegation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-571-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-571">deleg=\rho(id) \in Delegations</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-559-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-559">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-560-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-560">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-572-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-572">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-573-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-573">act=\rho(a) \in Activities</script>.
</li>
-<li>The agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-561-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-561">agent_2</script> acted for the agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-562-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-562">agent_1</script> with respect to
- the activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-563-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-563">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-564-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-564">actedFor(deleg) = (agent_2,agent_1,act)</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-574-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-574">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-575-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-575">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-565-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-565">match(W,deleg,attrs)</script>.
+<li>The agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-576-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-576">agent_2</script> acted for the agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-577-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-577">agent_1</script> with respect to
+ the activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-578-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-578">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-579-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-579">actedFor(deleg) = (agent_2,agent_1,act)</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-580-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-580">match(W,deleg,attrs)</script>.
</li></ol></div>
</section>
@@ -2307,10 +2361,10 @@
<p>
Derivation formulas can be of one of two forms:</p>
-<ul><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-566-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-566">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>, which specifies an
+<ul><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-581-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-581">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>, which specifies an
activity, generation and usage event. For convenience we call this
a <dfn id="dfn-precise-derivation">precise derivation</dfn>.</li>
- <li> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-567-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-567">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>, which does not
+ <li> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-582-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-582">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>, which does not
specify an activity, generation and usage event. For convenience we
call this an <dfn id="dfn-imprecise-derivation">imprecise derivation</dfn>.</li>
</ul>
@@ -2318,26 +2372,26 @@
<section id="precise">
<h5><span class="secno">4.4.10.1 </span> Precise </h5>
-<p>A precise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-568-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-568">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
+<p>A precise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-583-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-583">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
</p>
<div class="semantics" id="derivation-precise-semantics" data-count="30" data-title="Semantics 30 (derivation-precise-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#derivation-precise-semantics">Semantics 30 (derivation-precise-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-569-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-569">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</script> holds if and only if:</p>
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-584-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-584">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-570-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-570">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-571-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-571">deriv = \rho(id) \in Derivations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-585-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-585">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-586-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-586">deriv = \rho(id) \in Derivations</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-572-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-572">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-573-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-573">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-587-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-587">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-588-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-588">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-574-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-574">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-575-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-575">act = \rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-589-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-589">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-590-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-590">act = \rho(a) \in Activities</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-576-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-576">g</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-577-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-577">gen = \rho(g) \in Generations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-591-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-591">g</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-592-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-592">gen = \rho(g) \in Generations</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-578-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-578">u</script> denotes a use event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-579-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-579">\rho(u) \in Usages</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-593-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-593">u</script> denotes a use event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-594-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-594">use = \rho(u) \in Usages</script>.
</li>
<li>The derivation denotes a one-step derivation path linking the
-entities via the activity, generation and use: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-580-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-580">derivationPath(deriv) =
+entities via the activity, generation and use: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-595-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-595">derivationPath(deriv) =
ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</script>.
</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-581-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-581">match(W,deriv,attrs)</script>.</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-596-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-596">match(W,deriv,attrs)</script>.</li>
</ol>
</div>
</section>
@@ -2345,18 +2399,18 @@
<h5><span class="secno">4.4.10.2 </span> Imprecise </h5>
<p>
-An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-582-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-582">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
+An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-597-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-597">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
<div class="semantics" id="derivation-imprecise-semantics" data-count="31" data-title="Semantics 31 (derivation-imprecise-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#derivation-imprecise-semantics">Semantics 31 (derivation-imprecise-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-583-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-583">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-598-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-598">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-584-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-584">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-585-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-585">deriv = \rho(id) \in Derivations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-599-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-599">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-600-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-600">deriv = \rho(id) \in Derivations</script>.
</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-586-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-586">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-587-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-587">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script> .
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-601-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-601">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-602-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-602">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script> .
</li>
-<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-588-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-588">derivationPath(deriv)= ent_2 \cdot w \cdot ent_1</script> for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-589-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-589">w</script>.
+<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-603-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-603">derivationPath(deriv)= ent_2 \cdot w \cdot ent_1</script> for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-604-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-604">w</script>.
</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-590-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-590">match(W,deriv,attrs)</script>.
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-605-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-605">match(W,deriv,attrs)</script>.
</li></ol></div>
</section>
</section>
@@ -2365,17 +2419,17 @@
<h4><span class="secno">4.4.11 </span>Influence</h4>
<div class="semantics" id="influence-semantics" data-count="32" data-title="Semantics 32 (influence-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#influence-semantics">Semantics 32 (influence-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-591-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-591">W,\rho \models wasInfluencedBy(id,o_2,o_1,attrs)</script> holds if
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-606-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-606">W,\rho \models wasInfluencedBy(id,o_2,o_1,attrs)</script> holds if
and only if at least one of the following hold:</p>
<ol>
- <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-592-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-592">id</script> denotes an influence <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-593-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-593">inf = \rho(id) \in Influences</script>.
- </li><li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-594-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-594">o_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-595-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-595">o_2</script> denote objects <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-596-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-596">obj_1 = \rho(o_1) \in
- Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-597-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-597">obj_2= \rho(o_2)
+ <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-607-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-607">id</script> denotes an influence <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-608-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-608">inf = \rho(id) \in Influences</script>.
+ </li><li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-609-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-609">o_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-610-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-610">o_2</script> denote objects <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-611-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-611">obj_1 = \rho(o_1) \in
+ Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-612-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-612">obj_2= \rho(o_2)
\in Objects</script>.</li>
- <li>The influence <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-598-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-598">inf</script> links <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-599-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-599">o_2</script> with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-600-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-600">o_1</script>; that is,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-601-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-601">influenced(inf) = (o_2,o_1)</script>.
+ <li>The influence <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-613-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-613">inf</script> links <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-614-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-614">o_2</script> with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-615-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>o</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-615">o_1</script>; that is,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-616-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-616">influenced(inf) = (o_2,o_1)</script>.
</li>
- <li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-602-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-602">match(W,deriv,attrs)</script>.
+ <li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-617-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-617">match(W,deriv,attrs)</script>.
</li>
</ol>
@@ -2385,26 +2439,26 @@
<section id="specialization">
<h4><span class="secno">4.4.12 </span> Specialization </h4>
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-603-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-603">specializationOf(e_1,e_2)</script> relation indicates when one entity formula presents more specific aspects of another.
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-618-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-618">specializationOf(e_1,e_2)</script> relation indicates when one entity formula presents more specific aspects of another.
</p>
<div class="semantics" id="specialization-semantics" data-count="33" data-title="Semantics 33 (specialization-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#specialization-semantics">Semantics 33 (specialization-semantics)</a></div> <p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-604-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-604">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-619-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-619">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
<ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-605-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-605">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-606-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-606">e_2</script> are entity identifiers, denoting
- entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-607-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-607">ent_1
- = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-608-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-608">ent_2 = \rho(e_2) \in Entities</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-620-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-620">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-621-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-621">e_2</script> are entity identifiers, denoting
+ entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-622-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-622">ent_1
+ = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-623-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-623">ent_2 = \rho(e_2) \in Entities</script>.
</li>
<!--<li>$(ent_1,ent_2) \in SpecializationOf$.-->
- <li>The two entities present aspects of the same thing, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-609-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-609">thingOf(ent_1) = thingOf(ent_2)</script>.
-</li>
-<li>The events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-610-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-610">ent_1</script> is contained in that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-611-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-611">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-612-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-612">events(ent_1) \subseteq events(ent_2)</script>.
+ <li>The two entities present aspects of the same thing, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-624-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-624">thingOf(ent_1) = thingOf(ent_2)</script>.
</li>
-<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-613-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-613">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-614-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-614">value(ent_1,attr) \supseteq value(ent_2,attr)</script>.</li>
+<li>The events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-625-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-625">ent_1</script> are contained in those of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-626-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-626">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-627-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-627">events(ent_1) \subseteq events(ent_2)</script>.
+</li>
+<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-628-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-628">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-629-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-629">value(ent_1,attr) \supseteq value(ent_2,attr)</script>.</li>
<li>At least one of these inclusions is strict: that is, either
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-615-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊊</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-615">events(ent_1) \subsetneq events(ent_2)</script> or for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-616-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-616">attr</script> we have
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-617-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊋</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-617">value(ent_1,attr) \supsetneq value(ent_2,attr)</script>.
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-630-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊊</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-630">events(ent_1) \subsetneq events(ent_2)</script> or for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-631-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-631">attr</script> we have
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-632-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊋</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-632">value(ent_1,attr) \supsetneq value(ent_2,attr)</script>.
</li>
</ol>
</div>
@@ -2421,10 +2475,10 @@
</li></ol>
-->
<p>The second criterion says that the two Entities present (possibly different) aspects of
-the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-618-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-618">ent_1</script> and
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-619-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-619">ent_2</script> to have the same events (or that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-620-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-620">ent_2</script> can be larger).
-The last criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-621-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-621">ent_1</script> to have more defined attributes than
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-622-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-622">ent_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-623-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-623">ent_2</script>. Two
+the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-633-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-633">ent_1</script> and
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-634-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-634">ent_2</script> to have the same events (or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-635-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-635">events(ent_2)</script> can be larger).
+The last criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-636-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-636">ent_1</script> to have more defined attributes than
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-637-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-637">ent_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-638-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-638">ent_2</script>. Two
different entities that have the same attributes can also be related
by specialization. The fifth criterion (indirectly) ensures that
specialization is irreflexive.
@@ -2435,15 +2489,15 @@
<h4><span class="secno">4.4.13 </span> Alternate </h4>
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-624-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-624">alternateOf</script> relation indicates when two entity formulas present (possibly different) aspects of the same thing. The two entities may or may not overlap in time.
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-639-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-639">alternateOf</script> relation indicates when two entity formulas present (possibly different) aspects of the same thing. The two entities may or may not overlap in time.
</p>
<div class="semantics" id="alternate-semantics" data-count="34" data-title="Semantics 34 (alternate-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#alternate-semantics">Semantics 34 (alternate-semantics)</a></div>
<p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-625-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-625">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-640-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-640">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
<ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-626-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-626">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-627-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-627">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-628-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-628">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-629-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-629">ent_2 = \rho(e_2)</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-641-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-641">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-642-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-642">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-643-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-643">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-644-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-644">ent_2 = \rho(e_2)</script>.
</li>
-<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-630-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-630">thingOf(ent_1) = thingOf(ent_2)</script>
+<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-645-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-645">thingOf(ent_1) = thingOf(ent_2)</script>
</li></ol>
</div>
@@ -2455,17 +2509,17 @@
<h4><span class="secno">4.4.14 </span> Membership </h4>
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-631-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-631">hadMember</script> relation relates a collection to an element of the collection.
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-646-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-646">hadMember</script> relation relates a collection to an element of the collection.
</p>
<div class="semantics" id="membership-semantics" data-count="35" data-title="Semantics 35 (membership-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#membership-semantics">Semantics 35 (membership-semantics)</a></div>
<p>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-632-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-632">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-647-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-647">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
<ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-633-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-633">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-634-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-634">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-635-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-635">coll
- = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-636-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-636">ent = \rho(e) \in Entities</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-648-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-648">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-649-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-649">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-650-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-650">coll
+ = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-651-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-651">ent = \rho(e) \in Entities</script>.
</li>
-<li>The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-637-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-637">ent</script> is a member of the collection <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-638-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-638">coll</script>: that is,
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-639-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-639">(coll,ent) \in Contains</script>.
+<li>The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-652-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-652">ent</script> is a member of the collection <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-653-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-653">coll</script>: that is,
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-654-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">(</mo><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-654">ent \in members(coll)</script>.
</li></ol>
</div>
@@ -2484,20 +2538,20 @@
<section id="precedes-and-strictly-precedes">
<h4><span class="secno">4.5.1 </span>Precedes and Strictly Precedes</h4>
- <p>The precedes relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-640-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-640">x \precedes y</script> holds between two events, one taking
+ <p>The precedes relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-655-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-655">x \precedes y</script> holds between two events, one taking
place before (or simultaneously with) another. Its meaning is
defined in terms of the quasiordering on events specified by
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-641-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-641">\preceq</script>. The semantics of strictly precedes (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-642-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-642">x
- \strictlyPrecedes y</script>) is similar, only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-643-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-643">x</script> must take place strictly
- before <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-644-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-644">y</script>. It is interpreted as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-645-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≺</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-645">\prec</script>, which we recall is
- defined from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-646-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-646">\preceq</script> as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-647-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi><mtext> and </mtext><mi>y</mi><mo stretchy="false">⪯̸</mo><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-647">x \prec y \iff x \preceq y \text{ and } y
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-656-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-656">\preceq</script>. The semantics of strictly precedes (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-657-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-657">x
+ \strictlyPrecedes y</script>) is similar, only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-658-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-658">x</script> must take place strictly
+ before <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-659-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-659">y</script>. It is interpreted as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-660-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≺</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-660">\prec</script>, which we recall is
+ defined from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-661-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⪯</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-661">\preceq</script> as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-662-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi><mtext> and </mtext><mi>y</mi><mo stretchy="false">⪯̸</mo><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-662">x \prec y \iff x \preceq y \text{ and } y
\not\preceq x</script>.</p>
<div class="semantics" id="precedes-semantics" data-count="36" data-title="Semantics 36 (precedes-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#precedes-semantics">Semantics 36 (precedes-semantics)</a></div>
<ol>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-648-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-648">W,\rho \models x \precedes y</script> holds if and only if
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-649-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-649">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-650-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">⪯</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-650">\rho(x) \preceq\rho(y)</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-651-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-651">W,\rho \models x \strictlyPrecedes y</script> holds if and only if
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-652-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-652">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-653-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">≺</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-653">\rho(x) \prec \rho(y)</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-663-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-663">W,\rho \models x \precedes y</script> holds if and only if
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-664-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-664">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-665-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">⪯</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-665">\rho(x) \preceq\rho(y)</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-666-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext> </mtext><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-666">W,\rho \models x \strictlyPrecedes y</script> holds if and only if
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-667-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-667">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-668-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">≺</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-668">\rho(x) \prec \rho(y)</script>.</li>
</ol>
</div>
@@ -2511,7 +2565,7 @@
wasGeneratedBy(gen2; e, a2, 2012-11-16T16:05:00) //different date
</pre>
<p>This instance is valid, and must satisfy precedence constraints
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-654-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-654">gen_1 \precedes gen_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-655-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-655">gen_2 \precedes gen_1</script>, but this does not
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-669-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-669">gen_1 \precedes gen_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-670-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-670">gen_2 \precedes gen_1</script>, but this does not
imply anything about the relative orderings of the associated
times, or vice versa.
</p>
@@ -2521,11 +2575,11 @@
<section id="notnull">
<h4><span class="secno">4.5.2 </span>notNull</h4>
- <p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-656-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-656">notNull(x)</script> formula is used to specify that a value may not
- be the null value <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-657-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-657">\bot</script>. The symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-658-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-658">-</script> always denotes the null
- value (i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-659-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-659">\rho(-) = \bot</script>).
+ <p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-671-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-671">notNull(x)</script> formula is used to specify that a value may not
+ be the null value <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-672-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-672">\bot</script>. The symbol "<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-673-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-673">-</script>" always denotes the null
+ value (i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-674-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-674">\rho(-) = \bot</script>).
</p><div class="semantics" id="notNull-semantics" data-count="37" data-title="Semantics 37 (notNull-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#notNull-semantics">Semantics 37 (notNull-semantics)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-660-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-660">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-661-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">≠</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-661">\rho(e) \neq
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-675-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-675">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-676-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">≠</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-676">\rho(e) \neq
\bot</script>.
</p>
</div>
@@ -2535,21 +2589,20 @@
<section id="typeof">
<h4><span class="secno">4.5.3 </span>typeOf</h4>
- <p>The typing formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-662-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-662">typeOf(x,t)</script> constrains the type of the value of
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-663-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-663">x</script>. </p>
+ <p>The typing formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-677-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-677">typeOf(x,t)</script> constrains the type of the value of
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-678-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-678">x</script>. </p>
<div class="semantics" id="typeOf-semantics" data-count="38" data-title="Semantics 38 (typeOf-semantics)"><div class="ruleTitle"><a class="internalDFN" href="#typeOf-semantics">Semantics 38 (typeOf-semantics)</a></div>
- <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-664-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-664">W,\rho\models typeOf(e,entity)</script> holds if and only if
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-665-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-665">\rho(e) \in Entities</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-666-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-666">W,\rho\models typeOf(a,activity)</script> holds if and only if
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-667-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-667">\rho(a) \in Activities</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-668-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-668">W,\rho\models typeOf(ag,agent)</script> holds if and only if
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-669-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-669">\rho(ag) \in Agents</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-670-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-670">W,\rho\models typeOf(c,Collection)</script> holds if and only if
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-671-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-671">\rho(c) \in Collections</script>.</li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-672-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-672">W,\rho\models typeOf(c,EmptyCollection)</script> holds if and only if
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-673-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-673">\rho(c) \in Collections</script> and there is no <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-674-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-674">e \in Entities</script> such
- that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-675-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-675">(\rho(c),e) \in Contains</script>.</li>
+ <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-679-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-679">W,\rho\models typeOf(e,entity)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-680-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-680">\rho(e) \in Entities</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-681-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-681">W,\rho\models typeOf(a,activity)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-682-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-682">\rho(a) \in Activities</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-683-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-683">W,\rho\models typeOf(ag,agent)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-684-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-684">\rho(ag) \in Agents</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-685-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-685">W,\rho\models typeOf(c,Collection)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-686-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-686">\rho(c) \in Collections</script>.</li>
+ <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-687-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-687">W,\rho\models typeOf(c,EmptyCollection)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-688-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-688">\rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-689-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-689">members(\rho(c)=\emptyset</script>.</li>
</ol>
</div>
@@ -2566,14 +2619,14 @@
In this section we restate all of the inferences and constraints
of PROV-CONSTRAINTS in terms of first-order logic. For each, we
give a proof sketch showing why the inference or constraint is
- sound for reasoning about the naive semantics. We exclude the
+ sound for reasoning about the semantics. We exclude the
definitional rules in PROV-CONSTRAINTS because they are only
needed for expanding the abbreviated forms of PROV-N statements to
the logical formulas used here.</p>
<section id="inferences">
<h3><span class="secno">5.1 </span>Inferences</h3>
-<div class="inference" id="communication-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#communication-generation-use-inference">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-676-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-676">\begin{array}[t]{l}
+<div class="inference" id="communication-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#communication-generation-use-inference">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-690-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-690">\begin{array}[t]{l}
\forall id,a_2,a_1,attrs.~
\\
\qquad wasInformedBy(id,a_2,a_1,attrs)
@@ -2583,9 +2636,9 @@
\end{array}</script></div>
<div class="proof">
-<p> This follows immediately from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-677-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-677">wasInformedBy</script>.</p>
+<p> This follows immediately from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-691-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-691">wasInformedBy</script>.</p>
</div>
-<div class="inference" id="generation-use-communication-inference"><div class="ruleTitle"><a class="internalDFN" href="#generation-use-communication-inference">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-678-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-678">\begin{array}[t]{l}
+<div class="inference" id="generation-use-communication-inference"><div class="ruleTitle"><a class="internalDFN" href="#generation-use-communication-inference">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-692-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-692">\begin{array}[t]{l}
\forall gen,e,a_1,t_1,attrs_1,use,a_2,t_2,attrs_2.~
\\
\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(use,a_2,e,t_2,attrs_2)
@@ -2594,9 +2647,9 @@
\exists id.~wasInformedBy(id,a_2,a_1,[])
\end{array}</script></div>
<div class="proof">
-<p> This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-679-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-679">wasInformedBy</script> and <a href="#axiom1">Axiom 1</a>.</p>
+<p> This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-693-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-693">wasInformedBy</script> and <a href="#axiom1">Axiom 1</a>.</p>
</div>
-<div class="inference" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a class="internalDFN" href="#entity-generation-invalidation-inference">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-680-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-680">\begin{array}[t]{l}
+<div class="inference" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a class="internalDFN" href="#entity-generation-invalidation-inference">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-694-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-694">\begin{array}[t]{l}
\forall e,attrs.~
\\
\qquad entity(e,attrs)
@@ -2609,7 +2662,7 @@
<p> This follows from <a href="#axiom2">Axiom 2</a>, which
requires that generation and invalidation events exist for each entity.</p>
</div>
-<div class="inference" id="activity-start-end-inference"><div class="ruleTitle"><a class="internalDFN" href="#activity-start-end-inference">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-681-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-681">\begin{array}[t]{l}
+<div class="inference" id="activity-start-end-inference"><div class="ruleTitle"><a class="internalDFN" href="#activity-start-end-inference">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-695-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-695">\begin{array}[t]{l}
\forall a,t_1,t_2,attrs.~
\\
\qquad activity(a,t_1,t_2,attrs)
@@ -2625,7 +2678,7 @@
</div>
-<div class="inference" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-682-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-682">\begin{array}[t]{l}
+<div class="inference" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-696-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-696">\begin{array}[t]{l}
\forall id,a,e_1,a_1,t,attrs.~
\\
\qquad wasStartedBy(id,a,e_1,a_1,t,attrs)
@@ -2637,7 +2690,7 @@
<div class="proof">
<p>This follows from <a href="#axiom3">Axiom 3</a>.</p>
</div>
-<div class="inference" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-683-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-683">\begin{array}[t]{l}
+<div class="inference" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-697-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-697">\begin{array}[t]{l}
\forall id,a,e_1,a_1,t,attrs.~
\\
\qquad wasEndedBy(id,a,e_1,a_1,t,attrs)
@@ -2650,7 +2703,7 @@
<p>This follows from <a href="#axiom4">Axiom 4</a>.</p>
</div>
<div class="inference" id="derivation-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-use-inference">Inference 11 (derivation-generation-use-inference)</a></div>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-684-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-684">\begin{array}[t]{l}
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-698-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-698">\begin{array}[t]{l}
\forall id,e_2,e_1,a,gen_2,use_1,attrs.~
\\
\qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(id,e_2,e_1,a,gen_2,use_1,attrs)
@@ -2664,7 +2717,7 @@
</div>
<div class="inference" id="revision-is-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#revision-is-alternate-inference">Inference 12 (revision-is-alternate-inference)</a></div>
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-685-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-685">\begin{array}[t]{l}
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-699-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-699">\begin{array}[t]{l}
\forall id,e_1,e_2,a,g,u.~
\\
\qquad wasDerivedFrom(id,e_2,e_1,a,g,u,[prov:type = prov:Revision]))
@@ -2676,7 +2729,7 @@
<p> This follows from the semantics of derivation steps (precise or
imprecise) and <a href="#axiom5">Axiom 5</a>.</p>
</div>
-<div class="inference" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-686-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-686">\begin{array}[t]{l}
+<div class="inference" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-700-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-700">\begin{array}[t]{l}
\forall att,e,ag,attrs.~
\\
\qquad wasAttributedTo(att,e,ag,attrs)
@@ -2689,7 +2742,7 @@
attribution, by <a href="#axiom6">Axiom 6</a>.</p>
</div>
-<div class="inference" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-687-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-687">\begin{array}[t]{l}
+<div class="inference" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-701-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-701">\begin{array}[t]{l}
\forall id,ag_1,ag_2,a,attrs.~
\\
\qquad actedOnBehalfOf(id,ag_1,ag_2,a,attrs)
@@ -2698,74 +2751,76 @@
\exists id_1,pl_1,id_2,pl_2.~wasAssociatedWith(id_1,a,ag_1,pl_1,[]) \wedge wasAssociatedWith(id_2,a,ag_2,pl_2,[])
\end{array}</script></div>
<div class="proof">
- <p>This follows from the semantics of association and delegation, by <a href="#axiom7">Axiom 7</a>.</p>
- </div>
-<div class="inference" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-688-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-688">\begin{array}[t]{l}
+ <p>This follows from the semantics of association and delegation, by <a href="#axiom7">Axiom 7</a>.</p> </div>
+<div class="inference" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div>
+ <ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-702-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-702">\begin{array}[t]{l}
\forall id,e,a,t,attrs.~
\\
\qquad wasGeneratedBy(id,e,a,t,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,e,a,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-689-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-689">\begin{array}[t]{l}
+\end{array}</script>
+ </li>
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-703-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-703">\begin{array}[t]{l}
\forall id,a,e,t,attrs.~
\\
\qquad used(id,a,e,t,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,a,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-690-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-690">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-704-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-704">\begin{array}[t]{l}
\forall id,a_2,a_1,attrs.~
\\
\qquad wasInformedBy(id,a_2,a_1,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,a_2,a_1,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-691-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-691">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-705-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-705">\begin{array}[t]{l}
\forall id,a_2,e,a_1,t,attrs.~
\\
\qquad wasStartedBy(id,a_2,e,a_1,t,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-692-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-692">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-706-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-706">\begin{array}[t]{l}
\forall id,a_2,e,a_1,t,attrs.~
\\
\qquad wasEndedBy(id,a_2,e,a_1,t,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-693-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-693">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-707-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-707">\begin{array}[t]{l}
\forall id,e,a,t,attrs.~
\\
\qquad wasInvalidatedBy(id,e,a,t,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,e,a,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-694-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-694">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-708-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-708">\begin{array}[t]{l}
\forall id,e_2,e_1,a,g,u,attrs.~
\\
\qquad wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,e_2,e_1,attrs)
-\end{array}</script></li><li>
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-695-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-695">\begin{array}[t]{l}
+\end{array}</script></li><li><br>
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-709-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-709">\begin{array}[t]{l}
\forall id,e,ag,attrs.~
\\
\qquad wasAttributedTo(id,e,ag,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,e,ag,attrs)
-\end{array}</script></li><li>
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-696-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-696">\begin{array}[t]{l}
+\end{array}</script></li><li><br>
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-710-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-710">\begin{array}[t]{l}
\forall id,a,ag,pl,attrs.~
\\
\qquad wasAssociatedWith(id,a,ag,pl,attrs)
\\
\quad\Rightarrow
wasInfluencedBy(id,a,ag,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-697-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-697">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-711-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-711">\begin{array}[t]{l}
\forall id,ag_2,ag_1,a,attrs.~
\\
\qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
@@ -2777,7 +2832,7 @@
<div class="proof">
<p>This follows via <a href="#axiom8">Axioms 8</a> through <a href="#axiom17">17</a>.
</p></div>
-<div class="inference" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-698-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-698">\begin{array}[t]{l}
+<div class="inference" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-712-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-712">\begin{array}[t]{l}
\forall e.~
\\
\qquad entity(e)
@@ -2786,10 +2841,10 @@
alternateOf(e,e)
\end{array}</script></div>
<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-699-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-699">ent = \rho(e)</script>. Clearly <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-700-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-700">ent \in Entities</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-701-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-701">thingOf(ent) = thingOf(ent)</script>, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-702-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-702">W,\rho \models alternateOf(e,e)</script>.</p>
+ <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-713-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-713">ent = \rho(e)</script>. Clearly <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-714-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-714">ent \in Entities</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-715-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-715">thingOf(ent) = thingOf(ent)</script>, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-716-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-716">W,\rho \models alternateOf(e,e)</script>.</p>
</div>
-<div class="inference" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-703-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-703">\begin{array}[t]{l}
+<div class="inference" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-717-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-717">\begin{array}[t]{l}
\forall e_1,e_2,e_3.~
\\
\qquad alternateOf(e_1,e_2) \wedge alternateOf(e_2,e_3)
@@ -2798,13 +2853,13 @@
alternateOf(e_1,e_3)
\end{array}</script></div>
<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-704-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-704">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-705-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-705">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-706-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-706">ent_3 = \rho(e_3)</script>. Then by
- assumption <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-707-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-707">ent_1</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-708-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-708">ent_2</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-709-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-709">ent_3</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-710-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-710">Entities</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-711-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-711">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-712-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-712">thingOf(e_2) = thingOf(e_3)</script>, so
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-713-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-713">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-714-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-714">W,\rho
+ <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-718-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-718">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-719-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-719">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-720-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-720">ent_3 = \rho(e_3)</script>. Then by
+ assumption <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-721-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-721">ent_1</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-722-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-722">ent_2</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-723-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-723">ent_3</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-724-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-724">Entities</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-725-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-725">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-726-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-726">thingOf(e_2) = thingOf(e_3)</script>, so
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-727-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-727">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-728-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-728">W,\rho
\models alternateOf(e_1,e_3)</script>.</p>
</div>
-<div class="inference" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-715-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-715">\begin{array}[t]{l}
+<div class="inference" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-729-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-729">\begin{array}[t]{l}
\forall e_1,e_2.~
\\
\qquad alternateOf(e_1,e_2)
@@ -2813,13 +2868,13 @@
alternateOf(e_2,e_1)
\end{array}</script></div>
<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-716-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-716">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-717-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-717">ent_2 = \rho(e_2)</script>. Then by
- assumption both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-718-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-718">ent_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-719-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-719">ent_2</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-720-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-720">Entities</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-721-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-721">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-722-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-722">W,\rho
+ <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-730-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-730">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-731-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-731">ent_2 = \rho(e_2)</script>. Then by
+ assumption both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-732-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-732">ent_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-733-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-733">ent_2</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-734-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-734">Entities</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-735-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-735">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-736-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-736">W,\rho
\models alternateOf(e_2,e_1)</script>.</p>
</div>
-<div class="inference" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-723-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-723">\begin{array}[t]{l}
+<div class="inference" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-737-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-737">\begin{array}[t]{l}
\forall e_1,e_2,e_3.~
\\
\qquad specializationOf(e_1,e_2) \wedge specializationOf(e_2,e_3)
@@ -2828,20 +2883,20 @@
specializationOf(e_1,e_3)
\end{array}</script></div>
<div class="proof">
- <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-724-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-724">ent_1</script> and
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-725-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-725">ent_2</script> and for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-726-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-726">ent_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-727-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-727">ent_3</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-728-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-728">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-729-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-729">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-730-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-730">ent_3 =
- \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-731-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-731">events(e_1) \subseteq events(e_2) \subseteq
+ <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-738-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-738">ent_1</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-739-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-739">ent_2</script> and for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-740-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-740">ent_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-741-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-741">ent_3</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-742-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-742">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-743-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-743">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-744-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-744">ent_3 =
+ \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-745-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-745">events(e_1) \subseteq events(e_2) \subseteq
events(e_3)</script>. Moreover,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-732-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-732">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-733-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-733">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-734-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-734">value(obj_1,attr)
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-746-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-746">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-747-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-747">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-748-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-748">value(obj_1,attr)
\supseteq value(obj_3,attr)</script>. Finally, at least one of the
- inclusions between <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-735-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-735">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-736-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-736">obj_2</script> is strict, so the same is the
- case for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-737-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-737">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-738-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-738">obj_3</script>.
+ inclusions between <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-749-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-749">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-750-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-750">obj_2</script> is strict, so the same is the
+ case for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-751-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-751">obj_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-752-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-752">obj_3</script>.
</p>
</div>
-<div class="inference" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-739-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-739">\begin{array}[t]{l}
+<div class="inference" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-753-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-753">\begin{array}[t]{l}
\forall e_1,e_2.~
\\
\qquad specializationOf(e_1,e_2)
@@ -2850,12 +2905,12 @@
alternateOf(e_1,e_2)
\end{array}</script></div>
<div class="proof">
- <p> If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-740-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-740">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-741-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-741">ent_2 = \rho(e_2)</script> are
- specializations, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-742-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-742">thingOf(ent_1) = thingOf(ent_2)</script>.
+ <p> If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-754-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-754">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-755-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-755">ent_2 = \rho(e_2)</script> are
+ specializations, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-756-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-756">thingOf(ent_1) = thingOf(ent_2)</script>.
</p>
</div>
-<div class="inference" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-743-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-743">\begin{array}[t]{l}
+<div class="inference" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-757-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-757">\begin{array}[t]{l}
\forall e_1,attrs,e_2.~
\\
\qquad entity(e_1,attrs) \wedge specializationOf(e_2,e_1)
@@ -2865,12 +2920,12 @@
\end{array}</script></div>
</section>
<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-744-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-744">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-745-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-745">ent_2 = \rho(e_2)</script>. Suppose
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-746-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>v</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-746">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-747-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-747">attrs</script>. Since
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-748-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-748">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-749-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-749">v \in value(ent_1,att)</script>.
- Thus <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-750-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-750">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-751-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-751">value(ent_2,att) \supseteq value(ent_1,att)</script>. Since
- this is the case for all attribute-value pairs in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-752-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-752">attrs</script>, and since
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-753-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-753">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-754-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-754">W,\rho \models entity(e_2,attrs)</script>.
+ <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-758-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-758">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-759-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-759">ent_2 = \rho(e_2)</script>. Suppose
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-760-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>v</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-760">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-761-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-761">attrs</script>. Since
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-762-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-762">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-763-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-763">v \in value(ent_1,att)</script>.
+ Thus <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-764-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-764">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-765-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-765">value(ent_2,att) \supseteq value(ent_1,att)</script>. Since
+ this is the case for all attribute-value pairs in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-766-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-766">attrs</script>, and since
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-767-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-767">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-768-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-768">W,\rho \models entity(e_2,attrs)</script>.
</p>
</div>
<section id="constraints">
@@ -2879,14 +2934,14 @@
<h4><span class="secno">5.2.1 </span>Uniqueness constraints</h4>
<div class="constraint" id="key-object"><div class="ruleTitle"><a class="internalDFN" href="#key-object">Constraint 22 (key-object)</a></div>
- <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-755-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-755">\forall
+ <ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-769-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-769">\forall
id,attrs_1,attrs_2. entity(id,attrs_1) \wedge entity(id,attrs_2)
\Rightarrow entity(id,attrs_1\cup attrs_2)</script></li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-756-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup></math></span></span></span><script type="math/tex" id="MathJax-Element-756">\forall
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-770-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>t</mi><mn>2</mn><mo>′</mo></msubsup></math></span></span></span><script type="math/tex" id="MathJax-Element-770">\forall
id,t_1,t_1',t_2,t_2',attrs_1,attrs_2.~ activity(id,t_1,t_2,attrs_1)
\wedge activity(id,t_1',t_2',attrs_2) \Rightarrow
activity(id,t_1,t_2,attrs_1\cup attrs_2) \wedge t_1=t_1' \wedge t_2=t_2'</script></li>
- <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-757-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-757">\forall
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-771-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⇒</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-771">\forall
id,attrs_1,attrs_2. agent(id,attrs_1) \wedge agent(id,attrs_2)
\Rightarrow agent(id,attrs_1\cup attrs_2)</script>.</li></ol></div>
<div class="proof">
@@ -2895,7 +2950,7 @@
for the underlying data.</p>
</div>
<div class="constraint" id="key-properties"><div class="ruleTitle"><a class="internalDFN" href="#key-properties">Constraint 23 (key-properties)</a></div>
- <ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-758-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-758">\begin{array}[t]{l}
+ <ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-772-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-772">\begin{array}[t]{l}
\forall
id,e,e',a,a',t,t',attrs_1,attrs_2.~ \\
wasGeneratedBy(id,e,a,t,attrs)
@@ -2903,61 +2958,61 @@
\quad \Rightarrow
wasGeneratedBy(id,e,a,t,attrs_1 \cup attrs_2) \wedge e=e' \wedge
a=a' \wedge t = t'\end{array}</script></li>
- <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-759-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-759">\begin{array}[t]{l}\forall
+ <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-773-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-773">\begin{array}[t]{l}\forall
id,e,e',a,a',t,t',attrs_1,attrs_2.~ \\used(id,a,e,t,attrs)
\wedge used(id,a',e',t',attrs_2)\\ \quad \Rightarrow
used(id,a,e',t,attrs_1 \cup attrs_2) \wedge e=e' \wedge
a=a' \wedge t = t'
\end{array}</script></li>
- <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-760-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-760">\begin{array}[t]{l}\forall
+ <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-774-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-774">\begin{array}[t]{l}\forall
id,a_1,a_2,a_1',a_2',attrs_1,attrs_2.~ \\wasInformedBy(id,a_1,a_2,attrs)
\wedge wasInformedBy(id,a_1',a_2',attrs_2)\\ \Rightarrow
wasInformedBy(id,a_1,a_2,attrs_1 \cup attrs_2) \wedge a_1=a_1'
\wedge a_2=a_2'
\end{array}</script></li>
- <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-761-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-761">\begin{array}[t]{l}\forall
+ <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-775-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-775">\begin{array}[t]{l}\forall
id,e,e'a_1,a_2,a_1',a_2',t,t',attrs_1,attrs_2.~ \\wasStartedBy(id,a_2,e,a_1,t,attrs_1)
\wedge wasStartedBy(id,a_2',e',a_1',t',attrs_2)\\ \Rightarrow
wasStartedBy(id,a_2,e,a_1,t,attrs_1 \cup attrs_2) \wedge a_1=a_1'
\wedge e=e' \wedge
a_2=a_2' \wedge t = t'
\end{array}</script></li>
- <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-762-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-762">\begin{array}[t]{l}\forall
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-776-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-776">\begin{array}[t]{l}\forall
id,e,e'a_1,a_2,a_1',a_2',t,t',attrs_1,attrs_2.~ \\wasEndedBy(id,a_2,e,a_1,t,attrs_1)
\wedge wasEndedBy(id,a_2',e',a_1',t',attrs_2)\\ \Rightarrow
wasEndedBy(id,a_2,e,a_1,t,attrs_1 \cup attrs_2) \wedge a_1=a_1'
\wedge e=e' \wedge
a_2=a_2' \wedge t = t'
\end{array}</script></li>
- <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-763-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-763">\begin{array}[t]{l}\forall
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-777-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>t</mi><mo stretchy="false">=</mo><msup><mi>t</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-777">\begin{array}[t]{l}\forall
id,e,e',a,a',t,t',attrs_1,attrs_2.~ \\wasInvalidatedBy(id,e,a,t,attrs_1)
\wedge wasInvalidatedBy(id,e',a',t',attrs_2)\\ \Rightarrow
wasInvalidatedBy(id,e,a,t,attrs_1 \cup attrs_2) \wedge e=e' \wedge
a=a' \wedge t = t'
\end{array}</script></li>
- <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-764-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msup><mi>u</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>u</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>g</mi><mo stretchy="false">=</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>u</mi><mo stretchy="false">=</mo><msup><mi>u</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-764">\begin{array}[t]{l}\forall
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-778-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msup><mi>u</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>u</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>e</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>g</mi><mo stretchy="false">=</mo><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>u</mi><mo stretchy="false">=</mo><msup><mi>u</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-778">\begin{array}[t]{l}\forall
id,e_1,e_1',e_2,e_2',a,a',g,g',u,u',attrs_1,attrs_2.~ \\wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs_1)
\wedge wasDerivedFrom(id,e_2',e_1',a',g_2',u_1',attrs_2)\\ \Rightarrow
wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs_1 \cup attrs_2) \wedge e_1=e_1'\wedge e_2=e_2'\wedge a=a'\wedge g=g'\wedge u=u'
\end{array}</script></li>
- <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-765-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-765">\begin{array}[t]{l}\forall
+ <li><br> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-779-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>e</mi><mo stretchy="false">=</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-779">\begin{array}[t]{l}\forall
id,e,e',ag,ag',attrs_1,attrs_2.~ \\wasAttributedTo(id,e,ag,attrs_1)
\wedge wasAttributedTo(id,e',ag',attrs_2)\\ \Rightarrow
wasAttributedTo(id,e,ag,attrs_1 \cup attrs_2) \wedge e=e' \wedge ag = ag'
\end{array}</script></li>
- <li> <br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-766-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>p</mi><mi>l</mi><mo stretchy="false">=</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-766">\begin{array}[t]{l}\forall
+ <li> <br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-780-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi>a</mi><msup><mi>g</mi><mo>′</mo></msup><mo stretchy="false">∧</mo><mi>p</mi><mi>l</mi><mo stretchy="false">=</mo><mi>p</mi><msup><mi>l</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-780">\begin{array}[t]{l}\forall
id,a,a',ag,ag',pl,pl',attrs_1,attrs_2.~ \\wasAssociatedWith(id,a,ag,pl,attrs_1)
\wedge wasAssociatedWith(id,a',ag',pl',attrs_2)\\ \Rightarrow
wasAssociatedWith(id,a,ag,pl,attrs_1 \cup attrs_2) \wedge a=a'
\wedge ag=ag' \wedge pl=pl'
\end{array}</script></li>
- <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-767-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-767">\begin{array}[t]{l}\forall
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-781-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>a</mi><msubsup><mi>g</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><mi>a</mi><mo stretchy="false">=</mo><msup><mi>a</mi><mo>′</mo></msup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-781">\begin{array}[t]{l}\forall
id,ag_1,ag_1',ag_2,ag_2',a,a',attrs_1,attrs_2.~ \\actedOnBehalfOf(id,ag_2,ag_1,a,attrs_1)
\wedge actedOnBehalfOf(id,ag_2',ag_1',a',attrs_2)\\ \Rightarrow
actedOnBehalfOf(id,ag_2,ag_1,a,attrs_1 \cup attrs_2) \wedge
ag_1=ag_1' \wedge ag_2 = ag_2' \wedge a = a'
\end{array}</script></li>
- <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-768-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-768">\begin{array}[t]{l}\forall
+ <li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-782-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">∧</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">=</mo><msubsup><mi>o</mi><mn>2</mn><mo>′</mo></msubsup></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-782">\begin{array}[t]{l}\forall
id,o_1,o_2,o_1',o_2',attrs_1,attrs_2.~ \\wasInfluencedBy(id,o_2',o_1',attrs_1)
\wedge wasInfluencedBy(id,o_2',o_1',attrs_2)\\ \Rightarrow
wasInfluencedBy(id,o_2,o_1,attrs_1 \cup attrs_2) \wedge o_1=o_1'
@@ -2969,7 +3024,7 @@
semantics of the respective assertions, again because functions are
used for the underlying data.</p>
</div>
-<div class="constraint" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-769-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-769">\begin{array}[t]{l}
+<div class="constraint" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-783-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-783">\begin{array}[t]{l}
\forall gen_1,gen_2,e,a,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasGeneratedBy(gen_1,e,a,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a,t_2,attrs_2)
@@ -2982,7 +3037,7 @@
This follows from <a href="#axiom18">Axiom 18</a>.
</p>
</div>
-<div class="constraint" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-770-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-770">\begin{array}[t]{l}
+<div class="constraint" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-784-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-784">\begin{array}[t]{l}
\forall inv_1,inv_2,e,a,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasInvalidatedBy(inv_1,e,a,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a,t_2,attrs_2)
@@ -2995,7 +3050,7 @@
This follows from <a href="#axiom19">Axiom 19</a>.
</p>
</div>
-<div class="constraint" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-771-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-771">\begin{array}[t]{l}
+<div class="constraint" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-785-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-785">\begin{array}[t]{l}
\forall start_1,start_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasStartedBy(start_1,a,e_1,a_0,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_0,t_2,attrs_2)
@@ -3009,7 +3064,7 @@
</p>
</div>
-<div class="constraint" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-772-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-772">\begin{array}[t]{l}
+<div class="constraint" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-786-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-786">\begin{array}[t]{l}
\forall end_1,end_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasEndedBy(end_1,a,e_1,a_0,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_0,t_2,attrs_2)
@@ -3022,7 +3077,7 @@
This follows from <a href="#axiom21">Axiom 21</a>.
</p>
</div>
-<div class="constraint" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-773-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-773">\begin{array}[t]{l}
+<div class="constraint" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-787-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-787">\begin{array}[t]{l}
\forall start,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
\\
\qquad activity(a_2,t_1,t_2,attrs) \wedge wasStartedBy(start,a_2,e,a_1,t,attrs_1)
@@ -3032,11 +3087,11 @@
\end{array}</script></div>
<div class="proof">
<p>
- This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-774-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-774">wasStartedBy</script>, since the start times
+ This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-788-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-788">wasStartedBy</script>, since the start times
must both match that of the activity.
</p>
</div>
-<div class="constraint" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-775-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-775">\begin{array}[t]{l}
+<div class="constraint" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-789-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-789">\begin{array}[t]{l}
\forall end,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
\\
\qquad activity(a_2,t_1,t_2,attrs) \wedge wasEndedBy(end,a_2,e,a_1,t,attrs_1)
@@ -3046,7 +3101,7 @@
\end{array}</script></div>
<div class="proof">
<p>
- This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-776-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-776">wasEndedBy</script>, since the end times
+ This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-790-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-790">wasEndedBy</script>, since the end times
must both match that of the activity.
</p>
</div>
@@ -3056,7 +3111,7 @@
<h4><span class="secno">5.2.2 </span>Ordering constraints</h4>
-<div class="constraint" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-777-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-777">\begin{array}[t]{l}
+<div class="constraint" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-791-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-791">\begin{array}[t]{l}
\forall start,end,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
@@ -3069,7 +3124,7 @@
</p>
</div>
-<div class="constraint" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-778-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-778">\begin{array}[t]{l}
+<div class="constraint" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-792-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-792">\begin{array}[t]{l}
\forall start_1,start_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_2,t_2,attrs_2)
@@ -3082,7 +3137,7 @@
</p>
</div>
-<div class="constraint" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-779-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-779">\begin{array}[t]{l}
+<div class="constraint" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-793-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-793">\begin{array}[t]{l}
\forall end_1,end_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasEndedBy(end_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
@@ -3091,18 +3146,18 @@
end_1 \precedes end_2
\end{array}</script></div>
<div class="proof">
- <p>This follows from <a href="#axiom22">Axiom 22</a>.
+ <p>This follows from <a href="#axiom23">Axiom 23</a>.
</p>
</div>
-<div class="constraint" id="usage-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#usage-within-activity">Constraint 33 (usage-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-780-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-780">\begin{array}[t]{l}
+<div class="constraint" id="usage-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#usage-within-activity">Constraint 33 (usage-within-activity)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-794-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-794">\begin{array}[t]{l}
\forall start,use,a,e_1,e_2,a_1,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge used(use,a,e_2,t_2,attrs_2)
\\
\quad\Rightarrow
start \precedes use
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-781-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-781">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-795-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-795">\begin{array}[t]{l}
\forall use,end,a,e_1,e_2,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad used(use,a,e_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
@@ -3116,14 +3171,14 @@
</p>
</div>
-<div class="constraint" id="generation-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#generation-within-activity">Constraint 34 (generation-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-782-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-782">\begin{array}[t]{l}
+<div class="constraint" id="generation-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#generation-within-activity">Constraint 34 (generation-within-activity)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-796-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-796">\begin{array}[t]{l}
\forall start,gen,e_1,e_2,a,a_1,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen,e_2,a,t_2,attrs_2)
\\
\quad\Rightarrow
start \precedes gen
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-783-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-783">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-797-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-797">\begin{array}[t]{l}
\forall gen,end,e,e_1,a,a_1,t,t_1,attrs,attrs_1.~
\\
\qquad wasGeneratedBy(gen,e,a,t,attrs) \wedge wasEndedBy(end,a,e_1,a_1,t_1,attrs_1)
@@ -3137,7 +3192,7 @@
</p>
</div>
-<div class="constraint" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-784-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-784">\begin{array}[t]{l}
+<div class="constraint" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-798-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-798">\begin{array}[t]{l}
\forall id,start,end,a_1,a_1',a_2,a_2',e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
\\
\qquad wasInformedBy(id,a_2,a_1,attrs) \wedge wasStartedBy(start,a_1,e_1,a_1',t_1,attrs_1) \wedge wasEndedBy(end,a_2,e_2,a_2',t_2,attrs_2)
@@ -3146,14 +3201,15 @@
start \precedes end
\end{array}</script></div>
<div class="proof">
- <p>This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-785-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-785">wasInformedBy</script> and the
- previous two constraints, because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-786-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-786">wasInformedBy</script> implies the
- existence of intermediate generation and usage events linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-787-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-787">a_1</script>
- and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-788-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-788">a_2</script>.
+ <p>This follows from the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-799-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-799">wasInformedBy</script>, <a href="#axiom24">Axiom 24</a>, and the
+ previous two constraints, because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-800-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-800">wasInformedBy</script> implies the
+ existence of intermediate generation and usage events linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-801-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-801">a_1</script>
+ and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-802-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-802">a_2</script> through an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-803-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-803">e</script>. The generation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-804-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-804">e</script> must precede
+ its use.
</p>
</div>
-<div class="constraint" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-789-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-789">\begin{array}[t]{l}
+<div class="constraint" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-805-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-805">\begin{array}[t]{l}
\forall gen,inv,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -3163,11 +3219,11 @@
\end{array}</script></div>
<div class="proof">
- <p>This follows from <a href="#axiom23">Axiom 23</a>.
+ <p>This follows from <a href="#axiom24">Axiom 24</a>.
</p>
</div>
- <div class="constraint" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-790-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-790">\begin{array}[t]{l}
+ <div class="constraint" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-806-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-806">\begin{array}[t]{l}
\forall gen,use,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(use,a_2,e,t_2,attrs_2)
@@ -3181,7 +3237,7 @@
</p>
</div>
-<div class="constraint" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-791-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-791">\begin{array}[t]{l}
+<div class="constraint" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-807-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-807">\begin{array}[t]{l}
\forall use,inv,a_1,a_2,e,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad used(use,a_1,e,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -3195,7 +3251,7 @@
</p>
</div>
-<div class="constraint" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-792-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-792">\begin{array}[t]{l}
+<div class="constraint" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-808-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-808">\begin{array}[t]{l}
\forall gen_1,gen_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasGeneratedBy(gen_1,e,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
@@ -3209,7 +3265,7 @@
</p>
</div>
-<div class="constraint" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-793-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-793">\begin{array}[t]{l}
+<div class="constraint" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-809-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-809">\begin{array}[t]{l}
\forall inv_1,inv_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasInvalidatedBy(inv_1,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a_2,t_2,attrs_2)
@@ -3223,7 +3279,7 @@
</p>
</div>
-<div class="constraint" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-794-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-794">\begin{array}[t]{l}
+<div class="constraint" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-810-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-810">\begin{array}[t]{l}
\forall d,e_1,e_2,a,gen_2,use_1,attrs.~
\\
\qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(d,e_2,e_1,a,gen_2,use_1,attrs)
@@ -3237,7 +3293,7 @@
</p>
</div>
-<div class="constraint" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-795-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-795">\begin{array}[t]{l}
+<div class="constraint" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-811-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">strictlyPrecedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-811">\begin{array}[t]{l}
\forall d,gen_1,gen_2,e_1,e_2,a,a_1,a_2,g,u,t_1,t_2,attrs,attrs_1,attrs_2.~
\\
\qquad wasDerivedFrom(d,e_2,e_1,a,g,u,attrs) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
@@ -3251,14 +3307,14 @@
</p>
</div>
-<div class="constraint" id="wasStartedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-ordering">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-796-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-796">\begin{array}[t]{l}
+<div class="constraint" id="wasStartedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-ordering">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-812-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-812">\begin{array}[t]{l}
\forall gen,start,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasStartedBy(start,a,e,a_2,t_2,attrs_2)
\\
\quad\Rightarrow
gen \precedes start
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-797-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-797">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-813-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-813">\begin{array}[t]{l}
\forall start,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasStartedBy(start,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -3273,14 +3329,14 @@
</p>
</div>
-<div class="constraint" id="wasEndedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-ordering">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-798-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-798">\begin{array}[t]{l}
+<div class="constraint" id="wasEndedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-ordering">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-814-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-814">\begin{array}[t]{l}
\forall gen,end,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e,a_2,t_2,attrs_2)
\\
\quad\Rightarrow
gen \precedes end
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-799-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-799">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-815-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-815">\begin{array}[t]{l}
\forall end,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasEndedBy(end,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -3295,7 +3351,7 @@
</p>
</div>
-<div class="constraint" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-800-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-800">\begin{array}[t]{l}
+<div class="constraint" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-816-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-816">\begin{array}[t]{l}
\forall gen_1,gen_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad specializationOf(e_2,e_1) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
@@ -3307,13 +3363,13 @@
<div class="proof">
<p> This follows from <a href="#axiom24">Axiom 24</a> and the fact
- that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-801-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-801">e_2</script> specializes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-802-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-802">e_1</script> then all of the events of the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-803-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-803">e_2</script>
- are events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-804-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-804">e_1</script>. Thus, the generation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-805-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-805">e_1</script> precedes all
- events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-806-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-806">e_2</script>.
+ that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-817-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-817">e_2</script> specializes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-818-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-818">e_1</script> then all of the events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-819-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-819">e_2</script>
+ are events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-820-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-820">e_1</script>. Thus, the generation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-821-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-821">e_1</script> precedes all
+ events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-822-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-822">e_2</script>.
</p>
</div>
- <div class="constraint" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-807-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-807">\begin{array}[t]{l}
+ <div class="constraint" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-823-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-823">\begin{array}[t]{l}
\forall inv_1,inv_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad specializationOf(e_1,e_2) \wedge wasInvalidatedBy(inv_1,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e_2,a_2,t_2,attrs_2)
@@ -3324,34 +3380,34 @@
<div class="proof">
<p> This follows from <a href="#axiom25">Axiom 25</a> and the fact
- that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-808-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-808">e_2</script> specializes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-809-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-809">e_1</script> then all of the events of the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-810-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-810">e_2</script>
- are events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-811-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-811">e_1</script>. Thus, the invalidation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-812-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-812">e_1</script> follows all
- events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-813-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-813">e_2</script>.
+ that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-824-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-824">e_2</script> specializes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-825-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-825">e_1</script> then all of the events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-826-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-826">e_2</script>
+ are events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-827-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-827">e_1</script>. Thus, the invalidation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-828-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-828">e_1</script> follows all
+ events of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-829-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-829">e_2</script>.
</p>
</div>
-<div class="constraint" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAssociatedWith-ordering">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-814-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-814">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-815-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-815">\begin{array}[t]{l}
+<div class="constraint" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAssociatedWith-ordering">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-830-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-830">pl</script> may be a placeholder -.</p><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-831-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-831">\begin{array}[t]{l}
\forall assoc,start_1,inv_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag,a_2,t_2,attrs_2)
\\
\quad\Rightarrow
start_1 \precedes inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-816-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-816">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-832-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-832">\begin{array}[t]{l}
\forall assoc,gen_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
\\
\quad\Rightarrow
gen_1 \precedes end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-817-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-817">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-833-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-833">\begin{array}[t]{l}
\forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag,e_2,a_2,t_2,attrs_2)
\\
\quad\Rightarrow
start_1 \precedes end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-818-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-818">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-834-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-834">\begin{array}[t]{l}
\forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
\\
\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
@@ -3366,14 +3422,14 @@
</p>
</div>
-<div class="constraint" id="wasAttributedTo-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAttributedTo-ordering">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-819-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-819">\begin{array}[t]{l}
+<div class="constraint" id="wasAttributedTo-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAttributedTo-ordering">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-835-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-835">\begin{array}[t]{l}
\forall att,gen_1,gen_2,e,a_1,a_2,t_1,t_2,ag,attrs,attrs_1,attrs_2.~
\\
\qquad wasAttributedTo(att,e,ag,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
\\
\quad\Rightarrow
gen_1 \precedes gen_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-820-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-820">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-836-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-836">\begin{array}[t]{l}
\forall att,start_1,gen_2,e,e_1,a_1,a_2,ag,t_1,t_2,attrs,attrs_1,attrs_2.~
\\
\qquad wasAttributedTo(att,e,ag,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
@@ -3388,14 +3444,14 @@
</p>
</div>
-<div class="constraint" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a class="internalDFN" href="#actedOnBehalfOf-ordering">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-821-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-821">\begin{array}[t]{l}
+<div class="constraint" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a class="internalDFN" href="#actedOnBehalfOf-ordering">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-837-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-837">\begin{array}[t]{l}
\forall del,gen_1,inv_2,ag_1,ag_2,a,a_1,a_2,t_1,t_2,attrs,attrs_1,attrs_2.~
\\
\qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasGeneratedBy(gen_1,ag_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag_2,a_2,t_2,attrs_2)
\\
\quad\Rightarrow
gen_1 \precedes inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-822-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-822">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-838-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mtext> </mtext><mrow class="MJX-TeXAtom-REL"><mrow class="MJX-TeXAtom-ORD"><mtext mathvariant="normal">precedes</mtext></mrow></mrow><mtext> </mtext><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-838">\begin{array}[t]{l}
\forall del,start_1,end_2,ag_1,ag_2,a,a_1,a_2,e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
\\
\qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasStartedBy(start_1,ag_1,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag_2,e_2,a_2,t_2,attrs_2)
@@ -3416,133 +3472,133 @@
<section id="typing-constraints">
<h4><span class="secno">5.2.3 </span>Typing constraints</h4>
-<div class="constraint" id="typing"><div class="ruleTitle"><a class="internalDFN" href="#typing">Constraint 50 (typing)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-823-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-823">\begin{array}[t]{l}
+<div class="constraint" id="typing"><div class="ruleTitle"><a class="internalDFN" href="#typing">Constraint 50 (typing)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-839-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-839">\begin{array}[t]{l}
\forall e,attrs.~
\\
\qquad entity(e,attrs)
\\
\quad\Rightarrow
typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-824-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-824">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-840-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-840">\begin{array}[t]{l}
\forall ag,attrs.~
\\
\qquad agent(ag,attrs)
\\
\quad\Rightarrow
typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-825-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-825">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-841-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-841">\begin{array}[t]{l}
\forall a,t_1,t_2,attrs.~
\\
\qquad activity(a,t_1,t_2,attrs)
\\
\quad\Rightarrow
typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-826-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-826">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-842-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-842">\begin{array}[t]{l}
\forall u,a,e,t,attrs.~
\\
\qquad used(u,a,e,t,attrs)
\\
\quad\Rightarrow
typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-827-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-827">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-843-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-843">\begin{array}[t]{l}
\forall g,a,e,t,attrs.~
\\
\qquad wasGeneratedBy(g,e,a,t,attrs)
\\
\quad\Rightarrow
typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-828-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-828">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-844-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-844">\begin{array}[t]{l}
\forall inf,a_2,a_1,t,attrs.~
\\
\qquad wasInformedBy(inf,a_2,a_1,t,attrs)
\\
\quad\Rightarrow
typeOf(a_1,activity) \wedge typeOf(a_2,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-829-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-829">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-845-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-845">\begin{array}[t]{l}
\forall start,a_2,e,a_1,t,attrs.~
\\
\qquad wasStartedBy(start,a_2,e,a_1,t,attrs)
\\
\quad\Rightarrow
typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-830-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-830">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-846-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-846">\begin{array}[t]{l}
\forall end,a_2,e,a_1,t,attrs.~
\\
\qquad wasEndedBy(end,a_2,e,a_1,t,attrs)
\\
\quad\Rightarrow
typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-831-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-831">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-847-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-847">\begin{array}[t]{l}
\forall inv,a,e,t,attrs.~
\\
\qquad wasInvalidatedBy(inv,e,a,t,attrs)
\\
\quad\Rightarrow
typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-832-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-832">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-848-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-848">\begin{array}[t]{l}
\forall id,e_2,e_1,a,g_2,u_1,attrs.~
\\
\qquad notNull(a) \wedge notNull(g_2) \wedge notNull(u_1) \wedge wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)
\\
\quad\Rightarrow
typeOf(e_2,entity) \wedge typeOf(e_1,activity) \wedge typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-833-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-833">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-849-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-849">\begin{array}[t]{l}
\forall id,e_2,e_1,attrs.~
\\
\qquad wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)
\\
\quad\Rightarrow
typeOf(e_2,entity) \wedge typeOf(e_1,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-834-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-834">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-850-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-850">\begin{array}[t]{l}
\forall id,e,ag,attrs.~
\\
\qquad wasAttributedTo(id,e,ag,attrs)
\\
\quad\Rightarrow
typeOf(e,entity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-835-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-835">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-851-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-851">\begin{array}[t]{l}
\forall id,a,ag,pl,attrs.~
\\
\qquad notNull(pl) \wedge wasAssociatedWith(id,a,ag,pl,attrs)
\\
\quad\Rightarrow
typeOf(a,activity) \wedge typeOf(ag,agent) \wedge typeOf(pl,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-836-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-836">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-852-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-852">\begin{array}[t]{l}
\forall id,a,ag,attrs.~
\\
\qquad wasAssociatedWith(id,a,ag,-,attrs)
\\
\quad\Rightarrow
typeOf(a,activity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-837-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-837">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-853-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-853">\begin{array}[t]{l}
\forall id,ag_2,ag_1,a,attrs.~
\\
\qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
\\
\quad\Rightarrow
typeOf(ag_2,agent) \wedge typeOf(ag_1,agent) \wedge typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-838-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-838">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-854-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-854">\begin{array}[t]{l}
\forall e_2,e_1.~
\\
\qquad alternateOf(e_2,e_1)
\\
\quad\Rightarrow
typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-839-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-839">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-855-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-855">\begin{array}[t]{l}
\forall e_2,e_1.~
\\
\qquad specializationOf(e_2,e_1)
\\
\quad\Rightarrow
typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-840-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-840">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-856-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-856">\begin{array}[t]{l}
\forall c,e.~
\\
\qquad hadMember(c,e)
\\
\quad\Rightarrow
typeOf(c,Collection) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-841-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-841">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-857-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-857">\begin{array}[t]{l}
\forall c.~
\\
\qquad entity(c,[prov:type = prov:emptyCollection]))
@@ -3553,6 +3609,7 @@
<div class="proof">
<p>Each typing constraint follows immediately from well-formedness
criteria marked [WF] in the corresponding semantics for formulas.
+ The final constraint requires <a href="#axiom36">Axiom 36</a>.
</p>
</div>
</section>
@@ -3560,21 +3617,21 @@
<section id="impossibility-constraints">
<h4><span class="secno">5.2.4 </span>Impossibility constraints</h4>
-<div class="constraint" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a class="internalDFN" href="#impossible-unspecified-derivation-generation-use">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-842-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-842">\begin{array}[t]{l}
+<div class="constraint" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a class="internalDFN" href="#impossible-unspecified-derivation-generation-use">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-858-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-858">\begin{array}[t]{l}
\forall id,e_1,e_2,g,attrs.~
\\
\qquad notNull(g) \wedge wasDerivedFrom(id,e_2,e_1,-,g,-,attrs)
\\
\quad\Rightarrow
False
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-843-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-843">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-859-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-859">\begin{array}[t]{l}
\forall id,e_1,e_2,u,attrs.~
\\
\qquad notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,-,u,attrs)
\\
\quad\Rightarrow
False
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-844-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-844">\begin{array}[t]{l}
+\end{array}</script></li><li><br><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-860-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-860">\begin{array}[t]{l}
\forall id,e_1,e_2,g,u,attrs.~
\\
\qquad notNull(g) \wedge notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,g,u,attrs)
@@ -3584,10 +3641,10 @@
\end{array}</script></li></ol></div>
<div class="proof">
<p>Each part follows from the fact that the semantics of
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-845-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-845">wasDerivedFrom</script> only allows formulas to hold when either all three
- of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-846-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-846">a,g,u</script> are <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-847-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-847">-</script> (denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-848-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-848">\bot</script>) or none of them are.</p>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-861-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-861">wasDerivedFrom</script> only allows formulas to hold when either all three
+ of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-862-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-862">a,g,u</script> are "<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-863-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-863">-</script>" (denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-864-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-864">\bot</script>) or none of them are.</p>
</div>
-<div class="constraint" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-849-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-849">\begin{array}[t]{l}
+<div class="constraint" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-865-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-865">\begin{array}[t]{l}
\forall e.~
\\
\qquad specializationOf(e,e)
@@ -3597,11 +3654,11 @@
\end{array}</script></div>
<div class="proof">
<p>This follows from the fact that in the semantics of
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-850-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-850">specializationOf</script>, the requirement that one of the inclusions is
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-866-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-866">specializationOf</script>, the requirement that one of the inclusions is
strict implies that the two entities cannot be the same.
</p>
</div>
-<div class="constraint" id="impossible-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-property-overlap">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-851-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-851">r</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-852-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-852">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-853-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-853">r</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-854-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-854">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-855-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-855">\begin{array}[t]{l}
+<div class="constraint" id="impossible-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-property-overlap">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-867-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-867">r</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-868-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-868">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-869-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-869">r</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-870-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-870">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-871-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-871">\begin{array}[t]{l}
\forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
\\
\qquad r(id,a_1,\ldots,a_m) \wedge s(id,b_1,\ldots,b_n)
@@ -3611,10 +3668,15 @@
\end{array}</script></div>
<div class="proof">
<p>This follows from the assumption that the different kinds of
- influences are disjoint sets, characterized by their types.
+ influences are disjoint sets, characterized by their types. Note
+ that generic influences are allowed to overlap with more specific
+ kinds of influence.
</p>
</div>
-<div class="constraint" id="impossible-object-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-object-property-overlap">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-856-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-856">p \in \{entity,activity,agent\}</script> and each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-857-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-857">r \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script>, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-858-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>p</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-858">\begin{array}[t]{l}
+<div class="constraint" id="impossible-object-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-object-property-overlap">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-872-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-872">p \in
+ \{entity,activity,agent\}</script> and each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-873-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-873">r \in \{ used, wasGeneratedBy,
+ wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy,
+ wasAttributedTo, wasAssociatedWith, actedOnBehalfOf, wasInfluencedBy\}</script>, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-874-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>p</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-874">\begin{array}[t]{l}
\forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
\\
\qquad p(id,a_1,\ldots,a_m) \wedge r(id,b_1,\ldots,b_n)
@@ -3627,7 +3689,7 @@
from other objects (entities, activities or agents).
</p>
</div>
-<div class="constraint" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-859-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-859">\begin{array}[t]{l}
+<div class="constraint" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-875-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-875">\begin{array}[t]{l}
\forall id.~
\\
\qquad typeOf(id,entity) \wedge typeOf(id,activity)
@@ -3639,7 +3701,7 @@
<p>This follows from the assumption that entities and activities are disjoint.
</p>
</div>
-<div class="constraint" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-860-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>s</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-860">\begin{array}[t]{l}
+<div class="constraint" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-876-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext> </mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>s</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-876">\begin{array}[t]{l}
\forall c,e.~
\\
\qquad hasMember(c,e) \wedge typeOf(c,EmptyCollection)
@@ -3649,8 +3711,8 @@
\end{array}</script></div>
<div class="proof">
<p>This follows from the definition of the semantics of
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-861-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-861">typeOf(c,EmptyCollection)</script>, which requires that there are no
- members of the collection denoted by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-862-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-862">c</script>.
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-877-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-877">typeOf(c,EmptyCollection)</script>, which requires that there are no
+ members of the collection denoted by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-878-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-878">c</script>.
</p>
</div>
</section>
@@ -3662,7 +3724,7 @@
<!--OddPage--><h2><span class="secno">6. </span>Soundness and Completeness</h2>
<p>Above we have presented arguments for the soundness of the
-constraints and inferences with respect to the naive semantics.
+constraints and inferences with respect to the semantics.
Here, we relate the notions of <dfn id="dfn-validity">validity</dfn> and <dfn id="dfn-normal-form">normal
form</dfn> defined in PROV-CONSTRAINTS to the semantics.
</p>
@@ -3673,35 +3735,39 @@
<p>Our main soundness result is:</p>
<div class="theorem" id="soundness-theorem" data-count="39" data-title="Theorem 39 (soundness-theorem)"><div class="ruleTitle"><a class="internalDFN" href="#soundness-theorem">Theorem 39 (soundness-theorem)</a></div>
- <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-863-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-863">W</script> be a PROV structure, that is, a structure providing all
+ <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-879-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-879">W</script> be a PROV structure, that is, a structure providing all
of the components above and satisfying all of
the axioms.</p>
<ol>
- <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-864-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-864">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-865-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-865">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-866-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-866">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-867-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-867">I</script> by applying one
- of the PROV inferences, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-868-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-868">W \models I'</script>.</li>
- <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-869-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-869">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-870-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-870">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-871-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-871">I</script> has a normal
- form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-872-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-872">I'</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-873-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-873"> W \models I'</script>.</li>
- <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-874-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-874">I</script> is a normal form and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-875-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-875">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-876-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-876">I</script> satisfies all of the ordering,
+ <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-880-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-880">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-881-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-881">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-882-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-882">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-883-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-883">I</script> by applying one
+ of the PROV inferences, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-884-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-884">W \models I'</script>.</li>
+<li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-885-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-885">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-886-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-886">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-887-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-887">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-888-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-888">I</script> by applying one
+ of the PROV key or uniqueness constraints, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-889-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-889">W \models I'</script>.</li>
+
+ <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-890-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-890">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-891-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-891">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-892-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-892">I</script> has a normal
+ form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-893-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-893">I'</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-894-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-894"> W \models I'</script>.</li>
+ <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-895-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-895">I</script> is a normal form and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-896-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-896">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-897-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-897">I</script> satisfies all of the ordering,
typing and impossibility constraints.
- </li><li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-877-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-877">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-878-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-878">I</script> is valid.</li>
+ </li><li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-898-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-898">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-899-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-899">I</script> is valid.</li>
</ol>
</div>
<div class="proof">
<p>For part 1, the arguments are as in the previous section. </p>
<p>For
- part 2, proceed by induction on a terminating sequence of inference
- or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-879-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-879">I</script> is in normal form then we are
- done. If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-880-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-880">I</script> is not in normal form then if an inference is applicable, then use part 1; if a uniqueness constraint is
- applicable, then from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-881-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-881">W \models I</script> the uniqueness constraint cannot
- fail on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-882-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-882">I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-883-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-883">W \models I'</script>, as argued for the key constraints in
- the previous section.</p>
+ part 2, if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-900-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-900">W \models I</script> then since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-901-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-901">W</script> satisfies the logical forms
+ of all uniqueness and kety constraints, constraint application cannot
+ fail on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-902-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-902">I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-903-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-903">W \models I'</script>.</p>
+ <p> For part 3, proceed by induction on a terminating sequence of inference
+ or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-904-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-904">I</script> is in normal form then we are
+ done. If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-905-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-905">I</script> is not in normal form then if an inference is applicable, then use part 1; if a uniqueness constraint is
+ applicable, then use part 2. </p>
<p>
- For part 3, the arguments are as
+ For part 4, the arguments are as
in the previous section for each constraint. </p>
- <p>Finally, for part 4,
- suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-884-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-884">W \models I</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-885-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-885">W \models I'</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-886-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-886">I'</script> is the normal
- form of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-887-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-887">I</script> by part 2. By part 3, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-888-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-888">I'</script> satisfies all of the
- remaining constraints, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-889-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-889">I</script> is valid.</p>
+ <p>Finally, for part 5,
+ suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-906-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-906">W \models I</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-907-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-907">W \models I'</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-908-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-908">I'</script> is the normal
+ form of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-909-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-909">I</script> by part 2. By part 3, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-910-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-910">I'</script> satisfies all of the
+ remaining constraints, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-911-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-911">I</script> is valid.</p>
</div>
</section>
@@ -3709,86 +3775,138 @@
<h3><span class="secno">6.2 </span>Weak Completeness</h3>
<p> In this section we give a translation from valid PROV instances to
- structures, and show that a valid PROV instance has a model.</p>
-
+ structures, and show that a valid PROV instance has a model. We
+ call this property <em>weak completeness</em>.
+
+ </p>
+
+ <div class="remark">
+ <p> The term <em>weak</em> refers to the fact that
+ there are still some inferences that are sound in the semantics but not
+ enforced by validation. For example, consider the following
+ (valid) PROV instance fragment:</p>
+ <pre>entity(e,[a=1])
+agent(e,[b=2])
+ </pre>
+ <p>This instance is valid and has a model, but in every model
+ satisfying the instance, it is also true that:</p>
+ <pre>entity(e,[a=1,b=2])
+agent(e,[a=1,b=2])
+ </pre>
+ <p>Thus, weak completeness captures the fact that every valid
+ instance has a model, but does not imply that a valid instance
+ satisfies all of the deductions possible in that model.
+ </p>
+ </div>
- <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-890-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-890">I</script> be a valid PROV instance that is in normal form.
- We define a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-891-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-891">M(I)</script> as follows, by giving the sets,
+ <p> Let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-912-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-912">I</script> be a valid PROV instance that is in normal form.
+ We define a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-913-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-913">M(I)</script> as follows, by giving the sets,
functions and relations specified in the components in <a href="#structures">Section 3</a>, and finally verifying that the
axioms hold.</p>
<p>First, without loss of generality, we assume that all times
- specified in activity or event formulas in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-892-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-892">I</script> are ground values.
- If not, set each variable in such a position to some dummy value.</p>
-
+ specified in activity or event formulas in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-914-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-914">I</script> are ground values.
+ If not, set each variable in such a position to some dummy value.
+ This is justified by the following fact:</p>
+
+<div class="lemma" id="time-grounding" data-count="40" data-title="Lemma 40 (time-grounding)"><div class="ruleTitle"><a class="internalDFN" href="#time-grounding">Lemma 40 (time-grounding)</a></div>
+ <p>
+ If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-915-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-915">I</script> is valid then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-916-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-916">S(I)</script> is valid, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-917-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-917">S</script> is any
+ substitution that maps time variables to time constants.
+ </p>
+ </div>
+ <div class="proof">
+ <p>
+ First, consider a substitution <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-918-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">=</mo><mo stretchy="false">[</mo><mi>t</mi><mo stretchy="false">:=</mo><mi>c</mi><mo stretchy="false">]</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-918">S = [t:=c]</script> that maps a
+ single time variable to a constant. It is straightforward to check
+ that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-919-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-919">I</script> is in normal form, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-920-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-920">S(I)</script> is in normal form, since
+ none of the inferences or uniqueness constraints can be enabled by
+ changing a time variable uniformly in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-921-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-921">I</script>. Similarly, the remaining
+ constraints are insensitive to the time values, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-922-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-922">S(I)</script> is in
+ normal form and satisfies all of the remaining constraints just as
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-923-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-923">I</script> does. The general case of a substitution that replaces multiple time variables
+ with constants is a straightforward generalization since we can view
+ such a substitution as a composition of single-variable substitutions.
+ </p>
+ </div>
+
<section id="sets">
<h4><span class="secno">6.2.1 </span>Sets</h4>
- <p> The sets of structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-893-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-893">M(I)</script> are: </p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-894-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>p</mi><mi>l</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">≠</mo><mo stretchy="false">−</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo stretchy="false">∣</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">∈</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow><mo>′</mo></msubsup><mo stretchy="false">∣</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>i</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>q</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>q</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-894">
+ <p> The sets of structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-924-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-924">M(I)</script> are: </p>
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-925-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>I</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>p</mi><mi>l</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">≠</mo><mo stretchy="false">−</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>c</mi><mo stretchy="false">∣</mo><mi>I</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mtext> or </mtext><mi>I</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>I</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow><mo>′</mo></msubsup><mo stretchy="false">∣</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>I</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>i</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">∣</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>E</mi><mi>n</mi><mi>d</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi mathvariant="normal">∃</mi><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext> </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>s</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-925">
\begin{eqnarray*}
- Entities &=& \{id \mid entity(id,attrs) \in I\}\\
- Plans &=& \{pl \mid wasAssociatedWith(id,ag,act,pl,attrs) \in I, pl
+ Entities &=& \{id \mid I \models typeOf(id,entity)\}\\
+ Plans &=& \{pl \mid \exists id,ag,ac,attrs.~ wasAssociatedWith(id,ag,act,pl,attrs) \in I, pl
\neq -\}\\
- Collections &=& \{e \mid hadMember(e',e) \in I\} \\
- &\cup& \{e \mid
- entity(e,attrs) \in I, prov:type=prov:emptyCollection \in attrs\}\\
+ Collections &=& \{c \mid I \models typeOf(c,prov:Collection) \text{
+ or } I \models typeOf(c,prov:EmptyCollection)\} \\
- Activities &=& \{id \mid activity(id,attrs) \in I\}\\
+ Activities &=& \{id \mid I \models typeOf(id, activity)\}\\
&\cup& \{a_{id},a'_{id} \mid id \in Entities\}\\
- &\cup& \{a_{id} \mid wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in I\}\\
- Agents &=& \{id \mid agent(id,attrs) \in I\}\\
+ &\cup& \{a_{id} \mid \exists id,e_2,e_1.~wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in I\}\\
+ Agents &=& \{id \mid I \models typeOf(id,agent)\}\\
\\
- Usages &=& \{id \mid used(id,a,e,t,attrs) \in I\}\\
- &\cup& \{u_{id} \mid wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
+ Usages &=& \{id \mid \exists a,e,t,attrs.~used(id,a,e,t,attrs) \in I\}\\
+ &\cup& \{u_{id} \mid \exists id,e_2,e_1,attrs.~wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
I\}\\
- Generations &=& \{id \mid wasGeneratedBy(id,e,a,t,attrs) \in I\}\\
- &\cup& \{g_{id} \mid wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
+ Generations &=& \{id \mid \exists e,a,t,attrs.~wasGeneratedBy(id,e,a,t,attrs) \in I\}\\
+ &\cup& \{g_{id} \mid \exists id,e_2,e_1,attrs.~wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
I\}\\
& \cup & \{g_{id} \mid id \in Entities\}\\
- Invalidations &=& \{id \mid wasInvalidatedBy(id,e,a,t,attrs) \in
+ Invalidations &=& \{id \mid \exists e,a,t,attrs.~wasInvalidatedBy(id,e,a,t,attrs) \in
I\}\\
& \cup & \{i_{id} \mid id \in Entities\}\\
- Starts &=& \{id \mid wasStartedBy(id,a,e,a',t,attrs) \in I\}\\
- Ends &=& \{id \mid wasEndedBy(id,a,e,a',t,attrs) \in I\}\\
+ Starts &=& \{id \mid \exists a,e,a',t,attrs.~wasStartedBy(id,a,e,a',t,attrs) \in I\}\\
+ Ends &=& \{id \mid \exists a,e,a',t,attrs.~wasEndedBy(id,a,e,a',t,attrs) \in I\}\\
Events &=& Usages \cup Generations \cup Invalidations \cup Starts
\cup Ends\\
\\
- Associations &=& \{id \mid wasAssociatedWith(id,ag,act,pl,attrs) \in
+ Associations &=& \{id \mid \exists ag,act,pl,attrs.~ wasAssociatedWith(id,ag,act,pl,attrs) \in
I\}\\
- Attributions &=& \{id \mid wasAttributedTo(id,e,ag,attrs) \in I\}\\
- Delegations &=& \{id \mid actedOnBehalfOf(id,ag_2,ag_1,act,attrs) \in I\}\\
- Communications &=& \{id \mid wasInformedBy(id,a_2,a_1,attrs) \in I\}\\
- Derivations &=& \{id \mid wasDerivedFrom(id,e_2,e_1,a,g,u,attrs) \in I\}\\
+ Attributions &=& \{id \mid \exists e,ag,attrs.~wasAttributedTo(id,e,ag,attrs) \in I\}\\
+ Delegations &=& \{id \mid \exists ag_2,ag_1,attrs.~ actedOnBehalfOf(id,ag_2,ag_1,act,attrs) \in I\}\\
+ Communications &=& \{id \mid \exists a_2,a_1,attrs.~wasInformedBy(id,a_2,a_1,attrs) \in I\}\\
+ Derivations &=& \{id \mid \exists e_2,e_1,a,g,u,attrs.~wasDerivedFrom(id,e_2,e_1,a,g,u,attrs) \in I\}\\
\\
Influences &=& Events \cup Associations \cup Attributions \cup
Communications \cup Delegations\\
- &\cup & \{id \mid wasInfluencedBy(id,q_2,q_1,attrs) \in I\}\\
+ &\cup & \{id \mid \exists o_2,o_1,attrs.~ wasInfluencedBy(id,o_2,o_1,attrs) \in I\}\\
\\
Objects &=& Entities \cup Activities \cup Agents \cup Influences\\
\end{eqnarray*}
</script>
-<p>In the definitions of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-895-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-895">Activities</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-896-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-896">Generations</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-897-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-897">Usages</script> we
- write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-898-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-898">a_{id}</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-899-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-899">g_{id}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-900-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-900">u_{id}</script> respectively to indicate
- additional activities, generations and usages added for imprecise derivations.
+<p>In the definitions of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-926-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-926">Entities</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-927-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-927">Collections</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-928-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-928">Activities</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-929-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-929">Agents</script> we use the notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-930-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-930">I \models typeOf(id,t)</script> to indicate
+ that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-931-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-931">id</script> must have type <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-932-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-932">t</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-933-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-933">I</script> according to the typing
+ constraints. For example, for entities, this means that the set
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-934-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-934">Entities</script> contains all identifiers <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-935-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-935">e,e'</script> appearing in the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-936-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-936">entity(e,attrs)</script>,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-937-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-937">alternateOf(e,e')</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-938-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-938">specializationOf(e,e')</script> formulas, as well as all tose
+ appearing in the appropriate positions of other formulas, as
+ specified in the typing constraints.
</p>
- <p> In addition, to define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-901-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-901">Things</script>, we introduce an
- equivalence relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-902-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-902">Entities</script> as follows:
+<p>In the definitions of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-939-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-939">Activities</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-940-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-940">Generations</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-941-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-941">Invalidations</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-942-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-942">Usages</script> we
+ write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-943-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-943">a_{id}</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-944-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-944">g_{id}</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-945-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>i</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-945">i_{id}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-946-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-946">u_{id}</script> respectively to indicate
+ additional activities, generations and usages added for imprecise
+ derivations or entities.
+</p>
+ <p> In addition, to define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-947-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-947">Things</script>, we introduce an
+ equivalence relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-948-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-948">Entities</script> as follows:
</p>
- <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-903-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">≡</mo><msub><mi>e</mi><mn>2</mn></msub><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-903">e_1 \equiv e_2 \iff alternateOf(e_1,e_2) \in I</script>
+ <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-949-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">≡</mo><msub><mi>e</mi><mn>2</mn></msub><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-949">e_1 \equiv e_2 \iff alternateOf(e_1,e_2) \in I</script>
<p>The fact that this is an equivalence relation follows from the
- fact that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-904-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-904">I</script> is in normal form, since the constraints on
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-905-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-905">alternateOf</script> ensure that it is an equivalence relation. Recall
- that given an equivalence relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-906-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-906">\equiv</script> on some set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-907-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-907">X</script>, the
- <em>equivalence class</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-908-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-908">x \in X</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-909-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>y</mi><mo stretchy="false">∈</mo><mi>X</mi><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">≡</mo><mi>y</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-909">[x]_\equiv = \{y
+ fact that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-950-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-950">I</script> is in normal form, since the constraints on
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-951-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-951">alternateOf</script> ensure that it is an equivalence relation. Recall
+ that given an equivalence relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-952-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-952">\equiv</script> on some set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-953-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-953">X</script>, the
+ <em>equivalence class</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-954-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-954">x \in X</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-955-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>y</mi><mo stretchy="false">∈</mo><mi>X</mi><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">≡</mo><mi>y</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-955">[x]_\equiv = \{y
\in X \mid x
- \equiv y\}</script>. The <em>quotient</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-910-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-910">X</script> by an equivalence
- relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-911-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-911">X</script> is the set of equivalence classes, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-912-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-912">X_\equiv =
+ \equiv y\}</script>. The <em>quotient</em> of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-956-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-956">X</script> by an equivalence
+ relation on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-957-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-957">X</script> is the set of equivalence classes, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-958-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>x</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-958">X_\equiv =
\{[x]_\equiv \mid x \in X\}</script>. Now we
- define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-913-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-913">Things</script> as the quotient of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-914-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-914">\equiv</script>-equivalence classes of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-915-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-915">Entities</script>.</p>
-
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-916-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msub><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">≡</mo></mrow></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-916">Things = Entities /_{\equiv} = \{[e]_\equiv \mid e \in Entities\}</script>
-
-<p> Observe that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-917-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-917">I</script> is normalized and valid, entities and
+ define the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-959-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-959">Things</script> as the quotient of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-960-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-960">\equiv</script>-equivalence classes of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-961-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-961">Entities</script>.</p>
+
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-962-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msub><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">≡</mo></mrow></msub><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">∣</mo><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-962">Things = Entities /_{\equiv} = \{[e]_\equiv \mid e \in Entities\}</script>
+
+<p> Observe that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-963-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-963">I</script> is normalized and valid, entities and
activities are disjoint, the influences are disjoint from entities,
activities, and agents,
and the different subsets of events and influences are pairwise
@@ -3797,10 +3915,8 @@
<section id="functions">
<h4><span class="secno">6.2.2 </span>Functions</h4>
-<p> First, we consider the functions associated with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-918-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-918">Entities</script>. We
-employ an auxiliary function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-919-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-919">events:Entities \to P(Events)</script> that collects the set of all
-events in which <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-920-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-920">e</script> participated.</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-921-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mi>e</mi></msub><mo stretchy="false">,</mo><msub><mi>i</mi><mi>e</mi></msub><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>v</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">=</mo><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo><mspace width="1em"></mspace><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">≠</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>n</mi><mi>i</mi><msub><mi>q</mi><mrow class="MJX-TeXAtom-ORD"><mi>e</mi></mrow></msub><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-921">
+<p> First, we consider the functions associated with <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-964-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-964">Entities</script>.</p>
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-965-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mi>e</mi></msub><mo stretchy="false">,</mo><msub><mi>i</mi><mi>e</mi></msub><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>v</mi><mo stretchy="false">∣</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">,</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">=</mo><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo fence="false" stretchy="false">}</mo><mspace width="1em"></mspace><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">≠</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>n</mi><mi>i</mi><msub><mi>q</mi><mrow class="MJX-TeXAtom-ORD"><mi>e</mi></mrow></msub><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">[</mo><mi>e</mi><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-965">
\begin{eqnarray*}
events'(e) &=& \{id \mid used(id,a,e,t,attrs) \in I\}\\
&\cup& \{id \mid wasGeneratedBy(id,e,a,t,attrs) \in I\}\\
@@ -3812,51 +3928,80 @@
value'(e,a) &=& \{v \mid entity(e,attrs) \in I, (a=v) \in attrs\}
\quad (a \neq uniq)\\
value'(e,uniq) &=&\{ uniq_{e}\}\\
-value(e,a) &=& value'(e) \cup \bigcup_{specializationOf(e',e) \in I} value'(e')\\
+value(e,a) &=& value'(e) \cup \bigcup_{specializationOf(e,e') \in I} value'(e')\\
thingOf(e) &=& [e]_\equiv
\end{eqnarray*}
</script>
-<p>Above, we introduce a fresh attribute name <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-922-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-922">uniq</script>, not already in
-use in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-923-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-923">I</script>, along with a fresh value <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-924-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-924">e</script> and for each entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-925-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-925">e</script> we
-add an attribute-value pair <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-926-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">=</mo><mi>u</mi><mi>n</mi><mi>i</mi><msub><mi>q</mi><mi>e</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-926">uniq=uniq_e</script> to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-927-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-927">values(e,uniq)</script>. This
+<p>Above, we introduce a fresh attribute name <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-966-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-966">uniq</script>, not already in
+use in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-967-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-967">I</script>, along with a fresh value <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-968-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-968">e</script> and for each entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-969-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-969">e</script> we
+add a value <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-970-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>n</mi><mi>i</mi><msub><mi>q</mi><mi>e</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-970">uniq_e</script> to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-971-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-971">values(e,uniq)</script>. This
construction ensures that if an entity is a specialization of another
-in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-928-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-928">I</script> then the specialization relationship will hold in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-929-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-929">M(I)</script>. We
-also define the set of all events involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-930-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-930">e</script> as the set of events
-immediately involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-931-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-931">e</script> or any specialization of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-932-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-932">e</script>. Similarly,
-the values of attributes of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-933-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-933">e</script> are those immediately declared for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-934-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-934">e</script>
-along with those of any specialization. We also introduce dummy
-generation and invalidation events for each entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-935-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-935">e</script>, along with
-activities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-936-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mi>e</mi></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mi>e</mi><mo>′</mo></msubsup></math></span></span></span><script type="math/tex" id="MathJax-Element-936">a_e,a'_e</script> to perform them.
+in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-972-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-972">I</script> then the specialization relationship will hold in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-973-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-973">M(I)</script>. We
+also define the set of all events involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-974-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-974">e</script> as the set of events
+immediately involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-975-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-975">e</script> or any specialization of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-976-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-976">e</script>. Similarly,
+the values of attributes of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-977-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-977">e</script> are those immediately declared for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-978-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-978">e</script>
+along with those of any <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-979-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>e</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-979">e'</script> that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-980-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-980">e</script> specializes. We also introduce dummy
+generation and invalidation events for each entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-981-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-981">e</script>, along with
+activities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-982-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mi>e</mi></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mi>e</mi><mo>′</mo></msubsup></math></span></span></span><script type="math/tex" id="MathJax-Element-982">a_e,a'_e</script> to perform them.
</p>
-<p> Similarly, for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-937-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-937">Things</script>, we
-employ an auxiliary function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-938-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-938">events:Things \to P(Events)</script> that collects the set of all
+<p> Similarly, for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-983-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-983">Things</script>, we
+employ an auxiliary function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-984-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-984">events:Things \to P(Events)</script> that collects the set of all
events in which one of the entities constituting the thing participated.</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-939-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-939">
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-985-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mo stretchy="false">∈</mo><mi>T</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-985">
\begin{eqnarray*}
events(T) &=& \bigcup_{e \in T} events(e)\\
value(T,a,evt) &=& \bigcup_{e \in T, evt \in events(e)} value(e,a)\\
\end{eqnarray*}
</script>
-<p> The functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-940-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-940">startTime</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-941-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-941">endTime</script> mapping activities to
- their start and end times is defined as follows:
+<p> The functions <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-986-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-986">events</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-987-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-987">startTime</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-988-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-988">endTime</script> mapping activities to
+ their start and end times are defined as follows:
</p>
- <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-942-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>t</mi><mn>1</mn></msub><mtext> where </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd></mtd><mtd><mtext> or </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>t</mi><mn>2</mn></msub><mtext> where </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd></mtd><mtd><mtext> or </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-942">\begin{eqnarray*}
+ <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-989-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mi>i</mi><mi>d</mi><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>g</mi><mi>e</mi></msub><mo stretchy="false">,</mo><msub><mi>i</mi><mi>e</mi></msub><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>t</mi><mn>1</mn></msub><mtext> where </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>t</mi><mn>2</mn></msub><mtext> where </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-989">\begin{eqnarray*}
+events(a) &=& \{id \mid used(id,a,e,t,attrs) \in I\}\\
+&\cup& \{id \mid wasGeneratedBy(id,e,a,t,attrs) \in I\}\\
+&\cup& \{id \mid wasInvalidatedBy(id,e,a,t,attrs) \in I\}\\
+&\cup& \{id \mid wasStartedBy(id,a,e,a',t,attrs) \in I\}\\
+&\cup& \{id \mid wasEndedBy(id,a,e,a',t,attrs) \in I\}\\
+&\cup& \{g_e,i_e\}\\
startTime(id) &=& t_1 \text{ where } activity(a,t_1,t_2,attrs) \in
I\\
- & \text{ or } wasStartedBy(start,a,e,a',t_1,attrs) \in I\\
endTime(id) &=& t_2 \text{ where } activity(a,t_1,t_2,attrs) \in
I\\
- & \text{ or } wasEndedBy(end,a,e,a',t_2,attrs) \in I\\
\end{eqnarray*}
</script>
- <p>Note that the above definition is deterministic because the start
- and end times in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-943-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-943">activity</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-944-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-944">wasStartedBy/wasEndedBy</script> statements
- must be equal.</p>
-<p> The function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-945-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-945">time</script> mapping <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-946-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-946">Events</script> to their <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-947-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-947">Times</script> is defined
+ <p>The start and end times are arbitrary (say, some zero value) for activities with no
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-990-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-990">activity</script> formula declaring the times. The above definitions of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-991-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-991">startTime</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-992-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-992">endTime</script> ignore any start times asserted in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-993-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-993">wasStartedBy</script> or
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-994-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-994">wasEndedBy</script> formulas. If both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-995-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-995">activity</script> and
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-996-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">/</mo></mrow><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-996">wasStartedBy/wasEndedBy</script> statements are present, then they must
+ match, but PROV-CONSTRAINTS does not require that the times of
+ multiple start or end events match for an activity with no
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-997-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-997">activity</script> statement.</p>
+
+<div class="remark">
+ <p>The following valid instance exemplifies the above discussion,
+ when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-998-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≠</mo><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-998">t_1 \neq t_2</script>:
+ </p>
+ <pre>wasStartedBy(id1;a,e1,a1,t1,[])
+wasStartedBy(id2;a,e2,a2,t2,[])
+</pre>
+<p>This instance becomes invalid if we add an <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-999-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-999">activity(a,[])</script>
+ statement, because it expands to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1000-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>T</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>T</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1000">activity(a,T_1,T_2,[])</script> where
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1001-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>T</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1001">T_1,T_2</script> are existential variables, and uniqueness constraints
+ require that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1002-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msub><mi>T</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1002">t_1 = T_1 = t_2</script>, which leads to uniqueness constraint failure.
+ </p>
+ </div>
+<p> For other <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1003-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1003">Objects</script> besides <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1004-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1004">Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1005-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1005">Activities</script>, the
+associated sets of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1006-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1006">Events</script> are defined to be empty. (An <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1007-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1007">Agent</script> that
+happens to be an <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1008-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1008">Entity</script> or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1009-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1009">Activity</script> will have the set of events
+defined above for the appropriate kind of object. Note that since
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1010-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1010">Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1011-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1011">Activities</script> are disjoint, this definition is unambiguous.)</p>
+
+<p> The function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1012-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1012">time</script> mapping <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1013-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1013">Events</script> to their <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1014-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1014">Times</script> is defined
as follows:
</p>
- <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-948-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-948">\begin{eqnarray*}
+ <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-1015-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>t</mi><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1015">\begin{eqnarray*}
time(id) &=& t \text{ where } used(id,a,e,t,attrs) \in I\\
time(id) &=& t \text{ where } wasGeneratedBy(id,e,a,t,attrs) \in I\\
time(id) &=& t\text{ where } wasInvalidatedBy(id,e,a,t,attrs) \in I\\
@@ -3864,12 +4009,13 @@
time(id) &=& t \text{ where }wasEndedBy(id,a,e,a',t,attrs) \in I\\
\end{eqnarray*}
</script>
+ <p>This definition is deterministic because the sets of identifiers
+ of different <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1016-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1016">Events</script> are disjoint, and the associated times are unique.</p>
-
- <p>Finally, the functions giving the interpretations of the
+ <p>The functions giving the interpretations of the
different identified influences are as follows:
</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-949-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mi>e</mi></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>i</mi><mi>e</mi></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mi>e</mi><mo>′</mo></msubsup><mo stretchy="false">)</mo><mtext> where </mtext><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd></mtr><mtr><mtd><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-949">\begin{eqnarray*}
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-1017-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mi>e</mi></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><msub><mi>i</mi><mi>e</mi></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><msubsup><mi>a</mi><mi>e</mi><mo>′</mo></msubsup><mo stretchy="false">)</mo><mtext> where </mtext><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></mtd></mtr><mtr><mtd><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mtext> where </mtext><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mtext> where </mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1017">\begin{eqnarray*}
used(id) &=& (a,e) \text{ where } used(id,a,e,t,attrs) \in I\\
used(u_{id}) &=& (a_{id},e_1) \text{ where } wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in I\\
generated(id) &=& (e,a) \text{ where }
@@ -3888,36 +4034,64 @@
communicated(id) &=& (a_2,a_1) \text{ where }
wasInformedBy(id,a_2,a_1,attrs)\in I\\
derivationPath(id) &=& e_2\cdot g \cdot a \cdot u \cdot e_1 \text{ where } wasDerivedFrom(id,e_2,e_1,a,g,u,attrs) \in I\\
- derivationPath(id) &=& e_2\cdot g_{id} \cdot a_{id} \cdot u_{id} \cdot e_1 \text{ where } wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in I\\
- \end{eqnarray*}
+ derivationPath(id) &=& e_2\cdot g_{id} \cdot a_{id} \cdot u_{id}
+ \cdot e_1 \text{ where } wasDerivedFrom(id,e_2,e_1,-,-,-,attrs) \in
+ I\\
+\end{eqnarray*}
</script>
- <p>Note that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-950-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-950">I</script> is normalized and valid, by the uniqueness
+ <p>Note that since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1018-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1018">I</script> is normalized and valid, by the uniqueness
constraints these functions are all well-defined. In the case for
imprecise derivations, we generate additional activities, generations
- and usages linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-951-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-951">e_2</script> to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-952-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-952">e_1</script>.
+ and usages linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1019-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1019">e_2</script> to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1020-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1020">e_1</script>.
</p>
+<p>The definition of the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1021-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1021">influenced</script> function is more involved, and
+is as follows:</p>
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-1022-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msup><mi>a</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>e</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">∈</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">∪</mo></mtd><mtd><mo fence="false" stretchy="false">{</mo><mo stretchy="false">(</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∣</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>o</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>o</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1022">\begin{eqnarray*}
+influenced(id) &=& used(id) \cup generated(id) \cup invalidated(id)\\
+&\cup& \{(a,e) \mid (a,e,a') \in started(id)\}\\
+&\cup& \{(a,e) \mid (a,e,a') \in ended(id)\}\\
+&\cup & \{(ag,act) \mid (ag,act,pl) \in associatedWith(id)\}\\
+ &\cup& attributedTo(id) \\
+&\cup & \{(ag_2,ag_1) \mid (ag_2,ag_1,act) \in actedFor(id)\}\\
+&\cup& communicated(id)\\
+&\cup& \{(e_2,e_1) \mid e_2 \cdot w \cdot e_1 \in
+ derivationPath(id)\}\\
+&\cup& \{(o_2,o_1) \mid wasInfluencedBy(id,o_2,o_1) \in I\}
+ \end{eqnarray*}
+</script>
+<p>This definition ensures that by construction <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1023-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1023">influenced(id)</script>
+contains all of the other associated relationships. For any specific
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1024-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1024">id</script>, however, most of the above sets will be empty, and the final
+line will often be redundant. It is not always redundant, because it
+is possible to assert an unspecified influence in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1025-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1025">I</script>.</p>
+
+<p> It is straightforward to verify (by their definitions) that the
+event sets associated with entities and activities satisfy the
+side-conditions in <a href="#events">Component 9</a>.</p>
+
+ <p> Finally, the collection membership function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1026-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1026">members</script> is
+ defined as follows:</p>
+ <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-1027-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mo stretchy="false">∣</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1027">members(c) = \{e \mid hadMember(c,e) \in I</script>
+
</section>
<section id="relations">
<h4><span class="secno">6.2.3 </span>Relations</h4>
-<p>We introduced a relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-953-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-953">\equiv</script> corresponding to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-954-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-954">alternateOf</script>
- above, in defining <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-955-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-955">Things</script>, but this relation is not a component of
+<p>We introduced a relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1028-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">≡</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1028">\equiv</script> corresponding to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1029-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1029">alternateOf</script>
+ above, in defining <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1030-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1030">Things</script>, but this relation is not a component of
the semantics.</p>
<p>The event ordering relation is defined as follows:</p>
- <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-956-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><msub><mi>G</mi><mi>I</mi></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-956">evt \preceq evt' \iff (evt,evt') \in G_I</script>
- <p> Here, we are using a slight abuse of notation: we write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-957-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>G</mi><mi>I</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-957">G_I</script>
- for the directed graph that is used during validation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-958-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-958">I</script> to
- test for cycles amond event ordering constraints. See Sec. 7.1 of PROV-CONSTRAINTS [<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>].</p>
-
- <p> Finally, the collection membership relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-959-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-959">Contains</script> is
- defined as follows:</p>
- <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-960-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>s</mi><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-960">(c,e) \in Contains \iff hadMember(c,e) \in I</script>
+ <span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-1031-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><msub><mi>G</mi><mi>I</mi></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1031">evt \preceq evt' \iff (evt,evt') \in G_I</script>
+ <p> closed under reflexivity and transitivity. Here, we are using a slight abuse of notation: we write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1032-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>G</mi><mi>I</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1032">G_I</script>
+ for the directed graph that is used during validation of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1033-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1033">I</script> to
+ test for cycles among event ordering constraints. See Sec. 7.1 of PROV-CONSTRAINTS [<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>].</p>
+
</section>
<section id="axioms-1">
<h4><span class="secno">6.2.4 </span>Axioms</h4>
- <p>To verify that the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-961-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-961">M(I)</script> yields a PROV
+ <p>To verify that the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1034-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1034">M(I)</script> yields a PROV
structure, we must ensure that all of the axioms and
side-conditions in the components are satisfied. As noted above,
the disjointness constraints are satisfied by construction. </p>
@@ -3925,25 +4099,25 @@
<p>For each axiom we give the corresponding justification:</p>
<ol><li>
- Axiom 1 follows because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-962-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-962">I</script> is normalized with respect to Inference 6.
+ Axiom 1 follows because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1035-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1035">I</script> is normalized with respect to Inference 6.
</li>
<li> Axiom 2 follows from the construction, since we add dummy
generation and invalidation events for every entity.</li>
<li>
-Axioms 3 and 4 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-963-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-963">I</script> is normalized with respect to
+Axioms 3 and 4 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1036-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1036">I</script> is normalized with respect to
Inference 9 and 10 respectively.
</li>
- <li>Axiom 5 follows because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-964-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-964">I</script> is normalized with respect to
+ <li>Axiom 5 follows because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1037-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1037">I</script> is normalized with respect to
Inference 12.
</li>
<li>
- Axioms 6 and 7 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-965-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-965">I</script> is normalized with respect to
+ Axioms 6 and 7 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1038-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1038">I</script> is normalized with respect to
Inference 13 and 14 respectively.
</li><li>
-Axioms 8 through 17 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-966-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-966">I</script> is normalized with respect to
+Axioms 8 through 17 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1039-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1039">I</script> is normalized with respect to
Inference 15.
</li><li>
-Axioms 18 through 21 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-967-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-967">I</script> is normalized with respect to
+Axioms 18 through 21 follow because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1040-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1040">I</script> is normalized with respect to
uniqueness constraints 24 through 27.
</li><li>
Axiom 22 follows because constraints 30, 31, 33, 34 ensure that a
@@ -3966,14 +4140,14 @@
</li>
<li>Axiom 26 follows from constraint 41.</li>
<li> Axiom 27 follows from constraint 42 and from the fact that the
- event ordering constraint graph <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-968-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>G</mi><mi>I</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-968">G_I</script> associated with a valid
- instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-969-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-969">I</script> cannot have any cycles involving a strict precedence
+ event ordering constraint graph <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1041-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>G</mi><mi>I</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1041">G_I</script> associated with a valid
+ instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1042-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1042">I</script> cannot have any cycles involving a strict precedence
edge.
</li>
<li> Axioms 28 through 31 follow from Constraint 47.</li>
<li> Axioms 32 and 33 follow from Constraint 48.</li>
<li> Axioms 34 and 35 follow from Constraint 49.</li>
-
+<li>Axiom 36 follows from Constraint 50, part 19, and the semantics of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1043-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>o</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1043">typeof</script>.</li>
</ol>
</section>
@@ -3981,62 +4155,113 @@
<h4><span class="secno">6.2.5 </span>Main results</h4>
<p> The main results of this section are that if a valid PROV instance
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-970-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-970">I</script> normalizes to
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-971-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-971">I'</script>, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-972-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><msup><mi>I</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-972">M(I') \models I</script>, and that furthermore <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-973-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><msup><mi>I</mi><mo>′</mo></msup><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-973">M(I')</script>
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1044-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1044">I</script> has a model <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1045-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1045">M \models I</script> that
satisfies all of the inferences and constraints. Thus, a form of
completeness holds: every valid PROV instance has a model.</p>
-<div class="theorem" id="weak-completeness-theorem" data-count="40" data-title="Theorem 40 (weak-completeness-theorem)"><div class="ruleTitle"><a class="internalDFN" href="#weak-completeness-theorem">Theorem 40 (weak-completeness-theorem)</a></div>
- <p>Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-974-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-974">J</script> is a valid PROV instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-975-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-975">I</script> is a normal form for
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-976-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-976">J</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-977-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-977">M(I) \models J</script>.</p>
+<div class="theorem" id="weak-completeness-theorem" data-count="41" data-title="Theorem 41 (weak-completeness-theorem)"><div class="ruleTitle"><a class="internalDFN" href="#weak-completeness-theorem">Theorem 41 (weak-completeness-theorem)</a></div>
+ <p>Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1046-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1046">J</script> is a valid PROV instance. Then there exists a PROV structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1047-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1047">M</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1048-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1048">M \models J</script>.</p>
</div>
<div class="proof">
<p>
- First, we consider the case where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-978-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-978">J</script> itself is a valid,
- normalized PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-979-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-979">I</script>, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-980-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-980">M(I)</script>
- be the corresponding structure. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-981-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-981">M(I)</script> is a PROV structure,
+ First, we consider the case where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1049-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1049">J</script> itself is a valid,
+ normalized PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1050-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1050">I</script>, with no existential variables, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1051-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1051">M(I)</script>
+ be the corresponding structure. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1052-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1052">M(I)</script> is a PROV structure,
satisfying all of the axioms (and hence all of the inferences and
constraints) stated above.
</p>
- <p>Moreover, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-982-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-982">M(I) \models I</script>, as can be verified on a
+ <p>Moreover, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1053-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1053">M(I) \models I</script>, as can be verified on a
case-by-case basis for each type of formula by considering its
- semantics and the definition of the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-983-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-983">M</script>. </p>
-
- <p> To conclude, we need to show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-984-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-984">J</script> is not in normal
- form, and normalizes to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-985-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-985">I</script>, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-986-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-986">M(I) \models J</script>. We can prove
+ semantics and the definition of the construction of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1054-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1054">M</script>. Most
+ cases are straightforward; we consider the cases of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1055-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1055">alternateOf</script>
+ and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1056-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1056">specializationOf</script> since they are among the most
+ interesting.</p>
+
+ <ul>
+ <li>Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1057-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1057">alternateOf(e_1,e_2) \in I</script>. We wish to show that
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1058-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1058">M(I) \models alternateOf(e_1,e_2)</script>. Since there are no
+ existential variables in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1059-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1059">I</script>, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1060-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">∈</mo><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo>.</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1060">e_1,e_2 \in
+ M(I).Entities</script>. Moreover, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1061-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">≡</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1061">e_1 \equiv e_2</script> according to the
+ equivalence relation defined above, and so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1062-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">[</mo><msub><mi>e</mi><mn>1</mn></msub><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mo stretchy="false">[</mo><msub><mi>e</mi><mn>2</mn></msub><msub><mo stretchy="false">]</mo><mo stretchy="false">≡</mo></msub><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1062">thingOf(e_1) =
+ [e_1]_\equiv = [e_2]_\equiv = thingOf(e_2)</script>, so we can conclude
+ that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1063-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1063">M(I) \models alternateOf(e_1,e_2)</script>.
+</li>
+<li>Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1064-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1064">specializationOf(e_1,e_2) \in I</script>. We wish to show that
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1065-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1065">M(I) \models specializationOf(e_1,e_2)</script>. Again, clearly
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1066-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1066">e_1,e_2 \in Entities</script>, and since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1067-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1067">I</script> satisfies all inferences,
+ we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1068-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1068">alternateOf(e_1,e_2)\in I</script> so clearly
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1069-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1069">thingOf(e_2) = thingOf(e_1)</script> as argued above. Next,
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-1070-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">⊆</mo></mtd><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><msup><mi>s</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>e</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1070">\begin{eqnarray*}
+events(e_1) &=& events'(e_1) \cup \bigcup_{specializationOf(e',e_1)
+ \in I} events'(e') \\
+&\subseteq& events'(e_2) \cup
+ \bigcup_{specializationOf(e',e_2) \in I} events'(e_2)\\
+&=&
+ events(e_2)
+\end{eqnarray*}
+</script>
+because <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1071-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1071">specializationOf(e_1,e_2) \in I</script> and all <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1072-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>e</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1072">e'</script> that are specializations of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1073-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1073">e_1</script> are also
+ specializations of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1074-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1074">e_2</script>.
+ Furthermore, for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1075-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1075">attr</script>,
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-1076-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="3pt" columnspacing="thickmathspace" displaystyle="true" side="right" minlabelspacing="0.8em"><mtr><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">⊇</mo></mtd><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><munder><mo stretchy="false">⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi></mrow></munder><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">(</mo><msup><mi>e</mi><mo>′</mo></msup><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">=</mo></mtd><mtd><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1076">\begin{eqnarray*}
+value(e_1,attr) &=& value'(e_1,attr) \cup
+ \bigcup_{specializationOf(e_1,e') \in I} value'(e',attr)\\
+ &\supseteq& value'(e_2,attr) \cup
+ \bigcup_{specializationOf(e_2,e')\in I}value'(e',attr)\\
+&=& value(e_2,attr)
+\end{eqnarray*}
+</script>
+for the same reason. Finally, by construction <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1077-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>n</mi><mi>i</mi><msub><mi>q</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>e</mi><mn>1</mn></msub></mrow></msub><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1077">uniq_{e_1} \in
+ value(e_1,uniq) </script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1078-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>n</mi><mi>i</mi><msub><mi>q</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>e</mi><mn>1</mn></msub></mrow></msub><mo stretchy="false">∉</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1078">uniq_{e_1} \notin value(e_2,uniq)</script> so the
+ inclusion is strict for the special attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1079-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>n</mi><mi>i</mi><mi>q</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1079">uniq</script>. Thus, we
+ have verified all of the conditions necessary to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1080-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1080">M(I)
+ \models specializationOf(e_1,e_2)</script>.
+</li>
+</ul>
+
+<p> Next, we show how to handle a normalized, valid <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1081-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1081">I</script> contains
+existential variables <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1082-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>n</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1082">x_1,\ldots,x_n</script>. Choose fresh constants <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1083-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>c</mi><mi>n</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1083">c_1,\ldots,c_n</script> of
+appropriate types for the existential variables and define <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1084-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>c</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1084">\rho(x_i)
+= c_i</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1085-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1085">M(\rho(I)) \models \rho(I)</script> by the above argument.
+Moreover, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1086-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1086">M(\rho(I)),\rho \models I</script>. So <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1087-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1087">M(\rho(I))</script> is itself the desired
+model.
+</p>
+
+<p> Finally, to handle the case where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1088-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1088">J</script> is an arbitrary valid instance, we need to show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1089-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1089">J</script> is not in normal
+ form, and normalizes to some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1090-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1090">I</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1091-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1091">M \models I</script>, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1092-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1092">M \models J</script>. We can prove
this by induction on the length of the sequence of normalization
- steps. The base case, when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-987-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-987">J = I</script>, is established already.
- Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-988-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-988">J</script> normalizes in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-989-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn></math></span></span></span><script type="math/tex" id="MathJax-Element-989">n+1</script> steps and we can perform one
- normalization step on it to obtain <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-990-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-990">J'</script>, which normalizes to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-991-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-991">I</script>
- in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-992-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-992">n</script> steps. By induction, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-993-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-993">M(I) \models J'</script>. For
- each possible normalization step, we must show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-994-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-994">M(I)
- \models J'</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-995-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-995">M(I) \models J</script>.
+ steps. The base case, when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1093-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1093">J = I</script>, is established already.
+ Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1094-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1094">J</script> normalizes in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1095-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn></math></span></span></span><script type="math/tex" id="MathJax-Element-1095">n+1</script> steps and we can perform one
+ normalization step on it to obtain <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1096-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1096">J'</script>, which normalizes to <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1097-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1097">I</script>
+ in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1098-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1098">n</script> steps. By induction, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1099-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1099">M \models J'</script>. For
+ each possible normalization step, we must show that if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1100-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1100">M
+ \models J'</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1101-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1101">M \models J</script>.
</p>
<p>First consider inference steps. These add information, that
- is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-996-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">⊇</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-996">J' \supseteq J</script>. Hence it is immediate that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-997-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-997">M(I) \models J</script>
- since every formula in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-998-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-998">J</script> is in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-999-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-999">J'</script>, and all formulas of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1000-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1000">J'</script>
- are satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1001-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1001">M(I)</script>.
+ is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1102-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">⊇</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1102">J' \supseteq J</script>. Hence it is immediate that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1103-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1103">M \models J</script>
+ since every formula in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1104-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1104">J</script> is in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1105-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1105">J'</script>, and all formulas of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1106-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1106">J'</script>
+ are satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1107-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1107">M</script>.
</p>
<p>Next consider uniqueness constraint steps, which may involve
- merging formulas. That is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1002-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1002">J = J_0 \cup
+ merging formulas. That is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1108-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo stretchy="false">=</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1108">J = J_0 \cup
\{r(id,a_1,\ldots,a_n,attrs_1), r(id,b_1,\ldots,b_n,attrs_2)\}</script>
- and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1003-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1003">J' = S(J_0) \cup \{r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
- attrs_2)\}</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1004-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1004">S</script> is a unifying substitution making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1005-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>b</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1005">S(a_i) =
- S(b_i)</script> for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1006-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1006">i \in \{1,\ldots,n\}</script>. Since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1007-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1007">M(I) \models J'</script>,
- we must have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1008-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1008">M(I),\rho \models J'</script> for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1009-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1009">\rho</script>, and therefore
- we must also have that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1010-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1010">M(I),\rho \models S(J_0)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1011-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1011">M(I),\rho \models r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
- attrs_2)</script>. We can extend <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1012-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1012">\rho</script> to a valuation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1013-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1013">\rho'</script> such that
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1014-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1014">M(I),\rho' \models S(x_1) = x_1 \wedge \cdots \wedge S(x_k) =
- x_k</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1015-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1015">dom(S) = \{x_1,\ldots,x_k\}</script>. Also,
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1016-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1016">M(I),\rho' \models J_0</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1017-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1017">M(I),\rho' \models r(id,a_1,\ldots,a_n,attrs_1\cup
- attrs_2)</script>. Moreover, since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1018-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1018">S</script> is a unifier, we also have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1019-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1019">M(I),\rho' \models r(id,b_1,\ldots,b_n,attrs_1\cup
+ and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1109-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>J</mi><mo>′</mo></msup><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1109">J' = S(J_0) \cup \{r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
+ attrs_2)\}</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1110-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1110">S</script> is a unifying substitution making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1111-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>b</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1111">S(a_i) =
+ S(b_i)</script> for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1112-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1112">i \in \{1,\ldots,n\}</script>. Since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1113-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1113">M \models J'</script>,
+ we must have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1114-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><msup><mi>J</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1114">M,\rho \models J'</script> for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1115-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1115">\rho</script>, and therefore
+ we must also have that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1116-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1116">M,\rho \models S(J_0)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1117-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1117">M,\rho \models r(id,S(a_1),\ldots,S(a_n),attrs_1\cup
+ attrs_2)</script>. We can extend <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1118-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1118">\rho</script> to a valuation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1119-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-1119">\rho'</script> such that
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1120-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><mi>S</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1120">M,\rho' \models S(x_1) = x_1 \wedge \cdots \wedge S(x_k) =
+ x_k</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1121-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1121">dom(S) = \{x_1,\ldots,x_k\}</script>. Also,
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1122-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-1122">M,\rho' \models J_0</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1123-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1123">M,\rho' \models r(id,a_1,\ldots,a_n,attrs_1\cup
+ attrs_2)</script>. Moreover, since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1124-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1124">S</script> is a unifier, we also have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1125-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">∪</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1125">M,\rho' \models r(id,b_1,\ldots,b_n,attrs_1\cup
attrs_2)</script>. Finally, since we can always remove attributes from an
atomic formula without damaging its satisfiability, we can
- conclude that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1020-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1020">M(I),\rho' \models r(id,a_1,\ldots,a_n,attrs_1)
+ conclude that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1126-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">,</mo><msup><mi mathvariant="italic">ρ</mi><mo>′</mo></msup><mo stretchy="false">⊨</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1126">M,\rho' \models r(id,a_1,\ldots,a_n,attrs_1)
\wedge r(id,b_1,\ldots,b_n, attrs_2)</script>. To conclude, we have
- shown <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1021-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1021">M(I) \models J_0 \cup \{ r(id,a_1,\ldots,a_n,attrs_1)
- r(id,b_1,\ldots,b_n, attrs_2)\}</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1022-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">(</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1022">M(I) \models J</script>, as
+ shown <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1127-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><msub><mi>J</mi><mn>0</mn></msub><mo stretchy="false">∪</mo><mo fence="false" stretchy="false">{</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-1127">M \models J_0 \cup \{ r(id,a_1,\ldots,a_n,attrs_1),
+ r(id,b_1,\ldots,b_n, attrs_2)\}</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-1128-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo stretchy="false">⊨</mo><mi>J</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-1128">M \models J</script>, as
desired.
</p>
</div></section>
@@ -4049,8 +4274,17 @@
<!--OddPage--><h2><span class="secno">A. </span>Acknowledgements</h2>
<p>
-This document has been produced by the PROV Working Group, and its contents reflect extensive discussion within the Working Group as a whole.
+This document has been produced by the PROV Working Group, and its
+ contents reflect extensive discussion within the Working Group
+ as a whole. Thanks specifically to Khalid Belhajjame, Tom De
+ Nies, Paolo
+ Missier, Simon Miles, Luc Moreau, Satya Sahoo, Jan van den
+ Bussche, and Joachim Van
+ Herwegen for detailed feedback.</p>
+<p>
+We would also like to acknowledge <a href="http://www.dagstuhl.de">Schloss Dagstuhl - Leibniz Center for Informatics</a>, because significant progress was made on this document at <a href="http://www.dagstuhl.de/en/program/calendar/semhp/?semnr=12091">Dagstuhl Seminar 12091 (Principles of Provenance)</a> that took place from February 26 to March 2, 2012.
</p>
+
<p>Thanks also to Robin Berjon for the ReSPec.js specification writing
tool and to MathJax for their LaTeX-to-HTML conversion tools, both of
which aided in the preparation of this document.</p>
@@ -4184,8 +4418,7 @@
-->
<!-- LocalWords: Thibodeau OpenLink Tilmes Zednik Zhao Yuting
-->
-<section id="references" class="appendix"><!--OddPage--><h2><span class="secno">B. </span>References</h2><section id="informative-references"><h3><span class="secno">B.1 </span>Informative references</h3><dl class="bibliography"><dt id="bib-Logic">[Logic]</dt><dd>W. E. Johnson. <a href="http://www.ditext.com/johnson/intro-3.html"><cite>Logic: Part III</cite></a>.1924. URL: <a href="http://www.ditext.com/johnson/intro-3.html">http://www.ditext.com/johnson/intro-3.html</a>
-</dd><dt id="bib-PROV-AQ">[PROV-AQ]</dt><dd>Graham Klyne; Paul Groth; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/"><cite>Provenance Access and Query</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/</a>
+<section id="references" class="appendix"><!--OddPage--><h2><span class="secno">B. </span>References</h2><section id="informative-references"><h3><span class="secno">B.1 </span>Informative references</h3><dl class="bibliography"><dt id="bib-PROV-AQ">[PROV-AQ]</dt><dd>Graham Klyne; Paul Groth; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/"><cite>Provenance Access and Query</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/">http://www.w3.org/TR/2013/NOTE-prov-aq-20130430/</a>
</dd><dt id="bib-PROV-CONSTRAINTS">[PROV-CONSTRAINTS]</dt><dd>James Cheney; Paolo Missier; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/"><cite>Constraints of the PROV Data Model</cite></a>. 30 April 2013, W3C Recommendation. URL: <a href="http://www.w3.org/TR/2013/REC-prov-constraints-20130430/">http://www.w3.org/TR/2013/REC-prov-constraints-20130430/</a>
</dd><dt id="bib-PROV-DC">[PROV-DC]</dt><dd>Daniel Garijo; Kai Eckert; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/"><cite>Dublin Core to PROV Mapping</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/">http://www.w3.org/TR/2013/NOTE-prov-dc-20130430/</a>
</dd><dt id="bib-PROV-DICTIONARY">[PROV-DICTIONARY]</dt><dd>Tom De Nies; Sam Coppens; eds. <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/"><cite>PROV Dictionary</cite></a>. 30 April 2013, W3C Note. URL: <a href="http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/">http://www.w3.org/TR/2013/NOTE-prov-dictionary-20130430/</a>
Binary file semantics/releases/NOTE-prov-sem-20130430/prov-sem.pdf has changed
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/final-khalid.txt Sun Apr 14 19:44:18 2013 +0200
@@ -0,0 +1,64 @@
+> 1. Is the purpose of the document clear and consistent with the working group's consensus about the semantics? If not, can you suggest clarifications or improvements?
+ >
+ > Yes
+ >
+ > 2. Are there minor issues that can be corrected easily prior to final release?
+ >
+ > Yes (see below)
+ >
+ > 3. Are there blocking issues that must be addressed prior to final release?
+ >
+ > No
+ >
+ > 4. ISSUE-579 requested that we incorporate an axiomatization using a more standard logic formalism e.g. first-order logic. The current draft attempts to address this. Can this issue be closed?
+ >
+ > Yes.
+ >
+ > 5. ISSUE-635 requested that we address the issues of soundness and completeness in the semantics. This is currently attempted, by generalizing the semantics (which unfortunately also decreases the connection to intuitive notions of time.) As a result, we have a soundness and weak completeness result stating that any valid PROV instance has a model and vice versa. Can this issue be closed?
+ >
+ > Yes.
+ >
+ >
+ >
+ > C1. In Section 1.1., it will be helpful to provide a reference to Naive Semantics.
+ >
+
+I'm not sure what you mean here. I've made other copies of "naive semantics" into links to this definition.
+
+If you mean refer to an external resource, please suggest one.
+
+ > C2. In Section 2.1, you state that "To allow for the fact that some
+ > attributes can have undefined or multiple values, we sometimes use the set P(Value), that is, the set of sets of values." For clarification, you may add here that you use empty sets for undefined values.
+
+There is a remark to this effect later, but it's good to signpost it.
+
+ >
+ > C3. In Section 3, you use the term component, which is also use in PROV-DM, but with different meaning. It is worth mentioning this.
+
+Done
+
+ >
+ > C4. In the first paragraph of Section 3.2, the correspondence between Things and Objects is not clear, although it is talked about. This confusion is then lifted later on in the same section, but I think it is worth saying something about this earlier.
+
+Done
+
+ >
+ > C5. In Section 3.3, component 14, I could not follow the 5th bullet, I suspect there is a variable that has not been declared.
+ >
+
+Do you mean additional axiom 5?
+
+I believe the unquantified variable was $w$, and I've clarified it. Basically it is a dummy variable for the stuff in between the beginning and end of a derivation path.
+
+
+ > C6. In component 15, I was wondering if the following inference is mentioned somewhere: "a path between two entities that is contained in a dervation path, is also a derivation path"
+ >
+
+No, there is no inference to this effect in PROV-CONSTRAINTS, so we do not assume it here.
+
+ > C7. In the sets of structures that are listed in Section 6.2.1, there are variables that are not bound in the set. Some of these variables are associated the imprecise derivation, but there are also others that are not. In particular, if you look at the second set in the union that define Activities, you will notice that aid and aid' are not bound.
+ >
+ >
+
+These are new activities, generations, invalidations, and usages associated with certain ids. The notations a_id and so on are explained later.
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/final-luc.txt Sun Apr 14 19:44:18 2013 +0200
@@ -0,0 +1,84 @@
+
+ > - abstract: PROv -> PROV
+
+Done
+
+ > - sotd paragraph: add the paragraph about feedback and errata.
+ >
+
+Done
+
+ > - section 1: paragraph 1: definition of provenance: cite prov-dm.
+ >
+
+Done
+
+ > - section 1.1: generation/invalidation -> generation, invalidation
+ >
+
+Done
+
+ > - section 1.1: make 'not' bold
+ > not a definitive specification of the ONLY semantics
+ > ->
+ > NOT a definitive specification of the ONLY semantics
+ >
+
+Done
+
+ >
+ > - I like the mapping to events.
+ >
+ > - remark in 3.2.4.6: assocated -> associated
+
+Done
+
+ >
+ > - remark in 3.2.4.6: I didn't understand the last paragraph of the
+ > remark. why is it there is no way to express multi step derivation
+ > path?
+
+There is no way to write a PROV instance whose ONLY models have multiple step derivations.
+
+ >
+ > - component 15 axioms: I was surprised to see a reference to things among
+ > the axioms (see axiom 5). But I guess, this is OK.
+ >
+
+This is because one of the constraints links revision and alternate in a semi-arbitrary way (that is, there is nothing about the way revisions are interpreted that forces this). There are other constraints about alternate but these follow from the way alternate is modeled.
+
+ >
+ > - section 3.3, remark: well spotted that we miss a constraint for
+ > invalidation.
+ > Did you identify it when proving properties?
+
+Yes
+
+ >
+ > - section 4.3.2. How is \rho(st) defined? what it 'st' is a constant
+ > or an identifier?
+
+"st" is an ordinary parameter, i.e. either a time value constant or an identifier denoting an unknown time.
+
+ >
+ > - section 6.2: for the reader, can you make explicit why this is "WEAK completness".
+ >
+
+addressed in a remark/lemma
+
+ > - just before 6.2.1: why can you set each time variable to some dummy value?
+ >
+ > Is it because once, you have established an instance is valid, then
+ > you have already unified all possible time variable to ground
+ > values. Then, instantiating any time variable can no longer break
+ > any constraints.
+
+Yes, and this is because time values (and their ordering) are "just data", and so their values are irrelevant.
+
+ >
+ > - 6.2.3:
+ >
+ > amond -> among
+ >
+ >
+Done
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/final-satya.txt Sun Apr 14 19:44:18 2013 +0200
@@ -0,0 +1,45 @@
+ >
+ >
+ > Please address the following review questions:
+ >
+ > 1. Is the purpose of the document clear and consistent with the working group's consensus about the semantics? If not, can you suggest clarifications or improvements?
+ >
+ > Yes the document is easy to follow.
+ >
+ > 2. Are there minor issues that can be corrected easily prior to final release?
+ > Yes, some minor points are listed below
+ >
+ > 3. Are there blocking issues that must be addressed prior to final release?
+ > No
+ >
+ > 4. ISSUE-579 requested that we incorporate an axiomatization using a more standard logic formalism e.g. first-order logic. The current draft attempts to address this. Can this issue be closed?
+ > Yes
+ >
+ > 5. ISSUE-635 requested that we address the issues of soundness and completeness in the semantics. This is currently attempted, by generalizing the semantics (which unfortunately also decreases the connection to intuitive notions of time.) As a result, we have a soundness and weak completeness result stating that any valid PROV instance has a model and vice versa. Can this issue be closed?
+ > Can be closed - was not able to review completeness properly (will need to cross-check with cited axioms in the Section 6.2.4).
+ >
+ > Minor issues:
+ > Section 1.1
+ > As Khalid pointed out, need to clarify or cite "Naive Semantics".
+
+Again, not sure what is intended here. Naive just means naive, i.e. there's no reason to believe that it is the only or best example.
+
+ >
+ > Section 2.1
+ > The two sentences together are a bit confusing "Identifiers may or may not be URIs. Identifiers are viewed as variables from the point of view of logic."
+ > If they are URIs they cannot be variables - I am not sure the statement about URIs is needed here.
+
+Removed the first sentence. The intent is to align the way people use URIs and sameAs in OWL with variables and equality here. But if saying less is less confusing I'm happy to do that.
+
+ >
+ > Section 2.3
+ > This may be nit picking, should "is a linear order" be replaced by more generic "partial order"?
+ >
+
+It doesn't matter; we never use the time ordering for anything anyway. I am thinking that timestamps (xsd:dateTime) is linearly ordered in the obvious way, but this doesn't imply anything about the ordering of the associated events, because we don't necessarily know e.g. that all the time stamps are in the same frame of reference/time zone.
+
+ > Section 4.4.12
+ > In the Remark "(or that of can be larger)" "larger" is not clear
+ >
+
+Fixed I hope.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/final-simon.txt Sun Apr 14 19:44:18 2013 +0200
@@ -0,0 +1,69 @@
+> Yes, the document seem clear and the semantics correct. I see no blocking issues, but some more minor ones below. The two issues mentioned seem fully addressed to my (shallow) knowledge of them.
+ >
+ > Abstract: "PROv" should be "PROV"
+
+Done
+
+ >
+ > Section 1.1: "Although it is a work in progress" (3rd paragraph) and "(as yet)" (fourth paragraph). Is this appropriate for the final release of the note?
+
+I've adjusted this. Basically, I'm a little uncomfortable with publishing something with "theorems" and "proofs" that hasn't been formally peer-reviewed. So I've removed the preliminary-sounding text above and added a paragraph just noting that the WG has reviewed it and it reflects a consensus but this hasn't been peer-reviewed as far as the formal content goes.
+
+
+ >
+ > Section 2.2: "a set Values... we sometimes use the set P(Value)" (Values vs Value)
+ >
+
+Fixed
+
+ > Section 2.3: "Times SUBSET Val" should be "Times SUBSET Values"
+ >
+
+Fixed
+
+
+ > Section 2.4: "a null symbol "-". Placeholder symbols - " -> They seem to be the same symbol except that null has quotes round it (though it doesn't when used later). Can this be clarified?
+ >
+
+The quotes are for rmphasis, since otherwise it looks strange in the text. So they should all be "-" when they occur in a sentence. Fixed.
+
+
+ > Section 3.1: "Each thing has an associates set of Events" -> "associated set of Events"
+ >
+
+Fixed
+
+ > Section 3.1, Component 1, point 3: "from things to sets of events." does not seem to explain the relation. Shouldn't it be "from things to the sets of events associated with those things."?
+ >
+
+Fixed "to associated sets of events"
+
+ > Section 3.2.4.1: "An Event is an influence whose events is a single time instant" -> I just couldn't interpret this statement. Are there one or several events (it is ungrammatical)? I assume when you say "whose events" you mean the events associated to the (influence) object, but if so, I think this could be rephrased to be clearer. It seems a circular definition, as "events" refers to elements of the set "Event", right? I think I would need some rephrasing to help understand what was intended.
+ >
+
+Sorry, this was due to a late search-and-replace replacing "time interval" with "set of events". Fixed to " instantaneous influence that relates an activity to an entity"
+
+ > Section 3.2.4.1: "relates an activity to an entity (which could be an agent)" -> should this be "(either of which could be an agent)"?
+
+Yes, fixed.
+
+ >
+ > Sections 4.4.*: Many of the rules use a mixture of "e" and "ent", "e1" and "ent1", "e2" and "ent2", and in Semantics 30, "ent2.gen.act.use.ent1" should be "e2.g.a.u.e1" I think.
+ >
+
+Actually, this is intentional: the rules generally use parameter names like e,a etc. for syntax, and then define ent = rho(e), act = rho(a), etc. as the semantic values associated to the symbols by rho. In particular, the derivation paths are paths of semantic entities, generations, activities, etc. and so we want to use ent2, gen, act, etc. there.
+
+ > Section 4.4.12: "The events of ent1 is contained" (ungrammatical)
+
+Fixed.
+
+ >
+ > Section 6.2.2: "the values of attributes of e are those immediately declared for e along with those of any specialization". Why? Isn't this the wrong way round? An entity's specialization has attribute values that the entity does not have (across its lifetime). I may have misunderstood the intent here.
+ >
+
+Yes ,this was backwards in the text, updated to "... of any $e'$ that $e$ specializes"
+
+ > Section 6.2.3: "amond" -> "among".
+ >
+
+Fixed.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/final-tom.txt Sun Apr 14 19:44:18 2013 +0200
@@ -0,0 +1,60 @@
+
+ > 1. Introduction:
+ > PROv -> PROV
+ > The semantics does not (as yet) cover --> The semantics do not (as yet) cover
+ >
+
+Fixed
+
+> 3.1
+ > an associates set of Events --> associated
+
+Fixed
+
+ >
+ > 3.2
+ > It is also possible to have two different objects that are indistinguishable by their attributes and time intervals --> did you mean events instead of time intervals?
+
+Fixed - incomplete search & replace.
+
+ >
+ > 3.2.1.2
+ > Just wondering why you decided to use a relation for contains here, whereas for the rest of the document, you use functions. Both are correct, but this is the only place a relation was used. (unless we missed something)
+
+Yes, that change seems like a win! (We do use relations for event ordering though.) much better for stating emptiness constraints.
+
+ >
+ > 3.2.2
+ > An activity is an object that encompasses a set of events. --> Earlier in the document an object is described as encompassing a set of events, so according to this, all objects would be activities.
+
+Well, this isn't an if and only if. But there is no reason to be so specific., clarified this.
+
+ > 3.2.4.1
+ > started(st)=(a,e,a′) implies start∈ --> st is undefined. Change to started(start)
+
+Fixed
+
+> 3.3
+ > 6. 'a' is undefined --> there exist gen, assoc and a
+
+Fixed
+
+ > Also, the remark about axioms 22 and 23 is correct, but why is it arguable? If the constraint exists, why leave invalidations out here? Does it break something else?
+ >
+
+If we omit invalidations, then the weak completeness result won't hold, or at least, I'm not sure how to prove it. Trying to come up with a counterexample.
+
+ > 4.3.2
+ > startTime/endTime(id): --> should be act instead of id
+
+Fixed
+
+
+ > 4.4.10.1 use event ρ(u)∈Usages. --> use event use = ρ(u) ∈Usages
+ >
+
+Fixed
+
+ > I see most of these have been fixed already after other reviews.
+ > Overall, it's a good document, and for the most part understandable if you know the basic syntax. Chapter 6 is harder to follow, especially if you're not that familiar with formal logic, or a bit rusty. (which is probably not the audience for this document anyway)
+ >
--- a/xml/schema/prov-dictionary.xsd Sun Apr 14 19:43:18 2013 +0200
+++ b/xml/schema/prov-dictionary.xsd Sun Apr 14 19:44:18 2013 +0200
@@ -28,8 +28,8 @@
<!-- Key-Entity Pair -->
<xs:complexType name="KeyEntityPair">
<xs:sequence>
+ <xs:element name="key" type="xs:anySimpleType" />
<xs:element name="entity" type="prov:IDRef" />
- <xs:element name="key" type="xs:anySimpleType" />
</xs:sequence>
</xs:complexType>
@@ -40,7 +40,7 @@
<xs:complexType name="DictionaryMembership">
<xs:sequence>
<xs:element name="dictionary" type="prov:IDRef"/>
- <xs:element name="keyEntityPair" type="prov:KeyEntityPair" maxOccurs="unbounded"/>
+ <xs:element name="keyEntityPair" type="prov:KeyEntityPair" minOccurs=1 maxOccurs="unbounded"/>
</xs:sequence>
</xs:complexType>
@@ -51,7 +51,7 @@
<xs:sequence>
<xs:element name="newDictionary" type="prov:IDRef"/>
<xs:element name="oldDictionary" type="prov:IDRef"/>
- <xs:element name="keyEntityPair" type="prov:KeyEntityPair" maxOccurs="unbounded"/>
+ <xs:element name="keyEntityPair" type="prov:KeyEntityPair" minOccurs=1 maxOccurs="unbounded"/>
<!-- prov attributes -->
<xs:element ref="prov:label" minOccurs="0" maxOccurs="unbounded"/>
<xs:element ref="prov:type" minOccurs="0" maxOccurs="unbounded"/>
@@ -67,7 +67,7 @@
<xs:sequence>
<xs:element name="newDictionary" type="prov:IDRef"/>
<xs:element name="oldDictionary" type="prov:IDRef"/>
- <xs:element name="key" type="xs:anySimpleType" maxOccurs="unbounded" />
+ <xs:element name="key" type="xs:anySimpleType" minOccurs=1 maxOccurs="unbounded" />
<!-- prov attributes -->
<xs:element ref="prov:label" minOccurs="0" maxOccurs="unbounded"/>
<xs:element ref="prov:type" minOccurs="0" maxOccurs="unbounded"/>
