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+ <title>Constraints of the Provenance Data Model</title>
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+</style><link rel="stylesheet" href="http://www.w3.org/StyleSheets/TR/W3C-CR"><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--></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>
+
+ </p>
+ <h1 class="title" id="title">Constraints of the Provenance Data Model</h1>
+
+ <h2 id="w3c-candidate-recommendation-11-december-2012"><abbr title="World Wide Web Consortium">W3C</abbr> Candidate Recommendation 11 December 2012</h2>
+ <dl>
+
+ <dt>This version:</dt>
+ <dd><a href="http://www.w3.org/TR/2012/CR-prov-constraints-20121211/">http://www.w3.org/TR/2012/CR-prov-constraints-20121211/</a></dd>
+ <dt>Latest published version:</dt>
+ <dd><a href="http://www.w3.org/TR/prov-constraints/">http://www.w3.org/TR/prov-constraints/</a></dd>
+
+
+ <dt>Latest editor's draft:</dt>
+ <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html</a></dd>
+
+
+ <dt>Test suite:</dt>
+ <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/testcases/process.html">http://dvcs.w3.org/hg/prov/raw-file/default/testcases/process.html</a></dd>
+
+
+ <dt>Implementation report:</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>
+
+
+
+ <dt>Previous version:</dt>
+ <dd><a href="http://www.w3.org/TR/2012/WD-prov-constraints-20120911/">http://www.w3.org/TR/2012/WD-prov-constraints-20120911/</a> <a href="diff-c.html">(colored-coded diff)</a></dd>
+
+
+ <dt>Editors:</dt>
+ <dd><a href="http://homepages.inf.ed.ac.uk/jcheney">James Cheney</a>, University of Edinburgh</dd>
+<dd><a href="http://www.cs.ncl.ac.uk/people/Paolo.Missier">Paolo Missier</a>, Newcastle University</dd>
+<dd><a href="http://www.ecs.soton.ac.uk/~lavm/">Luc Moreau</a>, University of Southampton</dd>
+
+
+ <dt>Author:</dt>
+ <dd><a href="http://users.ugent.be/~tdenies/">Tom De Nies</a>, IBBT - Ghent University</dd>
+
+
+ </dl>
+
+
+
+
+
+ <p class="copyright">
+ <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> ©
+ 2012
+
+ <a href="http://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup>
+ (<a href="http://www.csail.mit.edu/"><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>,
+ <a href="http://www.ercim.eu/"><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
+ <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved.
+ <abbr title="World Wide Web Consortium">W3C</abbr> <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>
+
+ <section id="abstract" class="introductory"><h2>Abstract</h2>
+<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. PROV-DM is the conceptual data model that forms a
+basis for the <abbr title="World Wide Web Consortium">W3C</abbr> provenance (PROV) family of specifications.
+<!--
+PROV-DM
+distinguishes core structures, forming the essence of provenance
+information, from extended structures catering for more specific uses
+of provenance. PROV-DM is organized in six components, respectively
+dealing with: (1) entities and activities, and the time at which they
+were created, used, or ended; (2) derivations of entities from
+entities; (3) agents bearing responsibility for entities that were
+generated and activities that happened; (4) a notion of bundle, a
+mechanism to support provenance of provenance; (5) properties to link
+entities that refer to the same thing; and, (6) collections forming a
+logical structure for its members.
+-->
+</p>
+
+
+<p> This document defines a subset of PROV instances called
+<i><a href="#dfn-valid" class="internalDFN">valid</a></i> PROV instances, by analogy with notions of
+validity for other Web standards.
+The intent of validation is ensure that a PROV instance represents a
+consistent history of objects and their interactions that is safe to
+use for the purpose of logical reasoning and other kinds of analysis.
+Valid PROV instances satisfy
+certain <a>definitions</a>, <a>inferences</a>, and
+<a>constraints</a>. These definitions, inferences, and constraints
+provide a measure of consistency checking for provenance and reasoning
+over provenance. They can also be used to <a title="normal
+form" href="#dfn-normal-form" class="internalDFN">normalize</a> PROV instances to forms that can easily be
+compared in order to determine whether two PROV instances are
+<a href="#dfn-equivalent" class="internalDFN">equivalent</a>. Validity and equivalence are also defined for PROV
+bundles (that is, named instances) and documents (that is, a toplevel
+instance together with zero or more bundles).</p>
+
+</section><section id="sotd" class="introductory"><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:
+<ul>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/">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/2012/WD-prov-primer-20121211/">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/2012/CR-prov-o-20121211/">PROV-O</a> (Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [<cite><a class="bibref" href="#bib-PROV-O">PROV-O</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/">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/2012/CR-prov-n-20121211/">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/2012/CR-prov-constraints-20121211/">PROV-CONSTRAINTS</a>
+(Recommendation), a set of constraints applying to the PROV data model
+(this document);</li>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/">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/2012/WD-prov-xml-20121211/">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>
+
+</ul>
+<h4 id="how-to-read-the-prov-family-of-documentation">How to read the PROV Family of Documentation</h4>
+<ul>
+<li>The primer is the entry point to PROV offering an introduction to the provenance model.</li>
+<li>The Linked Data and Semantic Web community should focus on PROV-O defining PROV classes and properties specified in an OWL2 ontology. For further details, PROV-DM and PROV-CONSTRAINTS specify the constraints applicable to the data model, and its interpretation. </li>
+<li>Developers seeking to retrieve or publish provenance should focus on PROV-AQ.</li>
+<li>Readers seeking to implement other PROV serializations
+should focus on PROV-DM and PROV-CONSTRAINTS. PROV-O and PROV-N offer examples of mapping to RDF and text, respectively.</li>
+</ul>
+
+
+ <p>
+ This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as a Candidate Recommendation.
+
+ This document is intended to become a <abbr title="World Wide Web Consortium">W3C</abbr> 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>).
+
+
+ <abbr title="World Wide Web Consortium">W3C</abbr> publishes a Candidate Recommendation to indicate that the document is believed
+ to be stable and to encourage implementation by the developer community. This
+ Candidate Recommendation is expected to advance to Proposed Recommendation no earlier than
+ 31 January 2012.
+
+ All feedback is welcome.
+ </p>
+
+ <p>
+ Publication as a Candidate Recommendation does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
+ This is a draft document and may be updated, replaced or obsoleted by other documents at
+ any time. It is inappropriate to cite this document as other than work in progress.
+ </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>
+
+
+
+
+</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</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="#validation-process-overview-1" 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="#changes-since-last-version" class="tocxref"><span class="secno">B. </span>Changes since last version</a></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>
+
+
+
+
+
+
+ <section id="introduction">
+ <!--OddPage--><h2><span class="secno">1. </span>Introduction<br>
+</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.
+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. This document defines a form of validation for provenance. </p>
+
+
+
+ <section id="conventions">
+<h3><span class="secno">1.1 </span>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" href="#bib-RFC2119">RFC2119</a></cite>].</p>
+
+<p>In this document, logical formulas contain variables written as
+ lower-case identifiers. Some of these variables are written
+ beginning with the underscore character <span class="name">_</span>, by convention, to indicate that they
+ appear only once in the formula. Such variables are
+ provided merely as an aid to the reader. </p>
+
+</section>
+
+
+<section id="purpose">
+
+<h3><span class="secno">1.2 </span>Purpose of this document</h3>
+
+<p>The PROV Data Model, PROV-DM, is a conceptual data model for provenance, which is
+realizable using different representations such as PROV-N and PROV-O.
+A PROV <a>instance</a> is a set of PROV statements.
+A PROV <a>document</a> is an instance
+together with zero or more <a>bundles</a>, or named instances. For
+example, a PROV document could be a .provn document, the result
+of a query, a triple store containing PROV statements in RDF, etc.
+The
+PROV-DM specification [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] imposes minimal requirements upon
+PROV instances. A <a href="#dfn-valid" class="internalDFN">valid</a> PROV instance corresponds to a
+consistent history of objects and interactions to which logical
+reasoning can be safely applied. PROV instances need not
+be <a href="#dfn-valid" class="internalDFN">valid</a>.
+The term <a href="#dfn-valid" class="internalDFN">valid</a> is chosen by analogy with
+notions of validity in other <abbr title="World Wide Web Consortium">W3C</abbr> specifications. This
+terminology differs from the usual meaning of "validity" in logic;
+our notion of validity of a PROV instance/document is closer to
+logical "consistency".
+</p>
+
+<p> This document specifies <em>definitions</em> of some
+provenance statements in terms of others, <em>inferences</em> over PROV instances
+that applications <em class="rfc2119" title="may">may</em> employ, and also defines a class of
+<a href="#dfn-valid" class="internalDFN">valid</a> PROV instances by specifying <em>constraints</em> that
+<a href="#dfn-valid" class="internalDFN">valid</a> PROV instances must satisfy. There are four kinds of
+constraints: <em>uniqueness constraints</em>, <em>event ordering
+constraints</em>, <em>impossibility constraints</em>, and <em>type
+constraints</em>.
+Further discussion
+of the semantics of PROV statements, which justifies the definitions, inferences
+and constraints, and relates the procedural specification approach
+taken here to a declarative specification, can be found in the formal semantics [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>].
+</p>
+
+<p>We define validity and equivalence in terms of a
+concept called <a title="normal form" href="#dfn-normal-form" class="internalDFN">normalization</a>. Definitions, inferences,
+and uniqueness constraints can be applied to <a title="normal
+form" href="#dfn-normal-form" class="internalDFN">normalize</a> PROV instances, and event ordering, typing, and
+impossibility constraints can be checked on the normal form to determine
+<a title="valid" href="#dfn-valid" class="internalDFN">validity</a>. Equivalence of two PROV
+instances can be determined by comparing their normal forms. For PROV
+documents, validity and equivalence amount to checking the validity or
+pairwise equivalence of their respective instances.
+</p>
+<p>
+This specification defines
+validity and equivalence procedurally, via an algorithm based on
+<a title="normal form" href="#dfn-normal-form" class="internalDFN">normalization</a>. Applications <em class="rfc2119" title="may">may</em> implement
+validity and equivalence checking using normalization, as outlined
+here. Applications <em class="rfc2119" title="may">may</em> also implement validation and equivalence
+checking in
+any other way as long as the same instances or documents are considered valid or
+equivalent, respectively.
+</p>
+
+<p> Checking validity or equivalence are <em class="rfc2119" title="recommended">recommended</em>, but not required, for
+applications compliant with PROV.
+Applications producing provenance <em class="rfc2119" title="should">should</em> ensure that it is
+<a href="#dfn-valid" class="internalDFN">valid</a>, and similarly applications consuming provenance <em class="rfc2119" title="may">may</em> reject provenance that is not <a href="#dfn-valid" class="internalDFN">valid</a>. Applications
+that are determining whether PROV instances or documents convey the same
+information <em class="rfc2119" title="should">should</em> check equivalence as specified here. As a
+guideline, applications should
+treat equivalent instances or documents in the same way. This is a
+guideline only, because meaning of "in the same way" is
+application-specific. For example, applications that manipulate the syntax of
+PROV instances in particular representations, such as pretty-printing
+or digital signing, have good reasons to treat syntactically
+different, but equivalent, documents differently.
+</p>
+</section>
+<section id="structure-of-this-document">
+<h3><span class="secno">1.3 </span>Structure of this document</h3>
+
+<p><a href="#rationale">Section 2</a> gives a brief rationale
+for the definitions, inferences and constraints.
+</p>
+<p>
+<a href="#compliance">Section 3</a> summarizes the
+requirements for compliance with this document, which are specified in
+detail in the rest of the document. </p>
+<p>
+<a href="#concepts">Section 4</a> defines basic concepts used in the
+rest of the specification. </p>
+
+<p> <a href="#inferences">Section 5</a> presents definitions and inferences. Definitions allow replacing shorthand notation in [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>]
+with more explicit and complete statements; inferences allow adding
+new facts representing implicit knowledge about the structure of
+provenance. </p>
+
+<p><a href="#constraints">Section 6</a> presents four kinds of constraints,
+<em>uniqueness</em> constraints that prescribe that certain statements
+must be unique within PROV <a>instances</a>,
+<em>event ordering</em> constraints that require that the records in a
+PROV <a>instance</a> are consistent with a sensible ordering of events
+relating the activities, entities and agents involved,
+<em>impossibility</em> constraints that forbid certain patterns of
+statements in valid PROV instances, and <em>type</em> constraints that
+classify the types of identifiers in valid PROV instances.
+</p>
+
+<p><a href="#normalization-validity-equivalence">Section 7</a> defines the notions
+of <a>validity</a>, <a>equivalence</a> and <a>normalization</a>.
+</p>
+
+
+
+</section>
+<section id="audience">
+<h3><span class="secno">1.4 </span> Audience </h3>
+
+<p> The audience for this document is the same as for [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>]: developers
+and users who wish to create, process, share or integrate provenance
+records on the (Semantic) Web. Not all PROV-compliant applications
+need to perform inferences or check validity when processing provenance.
+However, applications that create or transform provenance <em class="rfc2119" title="should">should</em>
+attempt to produce valid provenance, to make it more useful to other
+applications by ruling out nonsensical or inconsistent information.
+</p>
+
+<p>This document assumes familiarity with [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] and employs the
+[<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>] notation.
+</p>
+
+</section>
+</section>
+
+<section id="rationale" class="informative">
+<!--OddPage--><h2><span class="secno">2. </span>Rationale</h2><p><em>This section is non-normative.</em></p>
+<p> This section gives a high-level rationale that provides some
+ further background for the constraints, but does not affect the
+technical content of the rest of the specification.</p>
+
+<section id="entities-activities-and-agents">
+<h3><span class="secno">2.1 </span>Entities, Activities and Agents</h3><p><em>This section is non-normative.</em></p>
+<p>
+One of the central challenges in representing provenance information
+is how to deal with change. Real-world objects, information objects
+and Web resources change over time, and the characteristics that make
+them identifiable in a given situation are sometimes subject to change
+as well. PROV allows for things to be described
+in different ways, with different descriptions of their
+state.
+</p>
+
+<p>
+An entity is a thing one wants to provide provenance for
+and whose situation in the world is described by some fixed
+attributes. An entity has a <dfn id="lifetime">lifetime</dfn>,
+defined as the period
+between its <a title="entity generation event" href="#dfn-generation-event" class="internalDFN">generation event</a>
+and its <a title="entity invalidation event" href="#dfn-invalidation-event" class="internalDFN">invalidation event</a>.
+An entity's attributes are established when the entity is
+created and (partially) describe the entity's situation and state
+during the entirety of the entity's lifetime.</p>
+
+<p>
+A different entity (perhaps representing a different user or
+system perspective) may fix other aspects of the same thing, and its provenance
+may be different. Different entities that fix aspects of the same
+thing are called <em>alternates</em>, and the PROV relations of
+<span class="name">specializationOf</span> and <span class="name">alternateOf</span> can be used to link such entities.</p>
+
+<p>Besides entities, a variety of other PROV objects and relationships carry
+attributes, including activity, generation, usage, invalidation, start, end,
+communication, attribution, association, delegation, and
+derivation. Each object has an associated duration interval (which may
+be a single time point), and attribute-value pairs for a given object
+are expected to be descriptions that hold for the object's duration.
+</p>
+<p>
+However, the attributes of entities have special meaning because they
+are considered to be fixed aspects
+of underlying, changing things. This motivates constraints on
+<span class="name">alternateOf</span> and <span class="name">specializationOf</span> relating the attribute values of
+different entities.
+</p>
+
+<p>
+In order to describe the provenance of something during an interval
+ over which relevant attributes of the thing are not fixed, a PROV
+ instance would describe multiple entities, each with its own
+ identifier, <a href="#lifetime" class="internalDFN">lifetime</a>, and fixed attributes, and express dependencies between
+ the various entities using <i><a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a></i>. For example, in order to
+ describe the provenance of several versions of a document, involving
+ attributes such as authorship that change over time, one can use
+ different entities for the versions linked by appropriate
+ generation, usage, revision, and invalidation events.
+</p>
+
+<p>There is no assumption that the set of attributes listed in an
+<span class="name">entity</span> statement is complete, nor
+that the attributes are independent or orthogonal of each
+other. Similarly, there is no assumption that the attributes of an
+entity uniquely identify it. Two different entities that present the
+same aspects of possibly different things can have the same
+attributes; this leads to potential ambiguity, which is mitigated through the
+use of identifiers.</p>
+
+<p>An <a>activity</a>'s lifetime is delimited by its <a title="activity start
+event" href="#dfn-start-event" class="internalDFN">start</a> and its <a title="activity end event" href="#dfn-end-event" class="internalDFN">end</a>
+events. It occurs over
+an interval delimited by two <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous
+events</a>. However, an activity statement need not mention start or end time information, because they may not be known.
+An activity's attribute-value pairs are expected to describe the activity's situation during its lifetime.
+</p>
+
+
+
+<p>An activity is not an entity. Indeed, an entity exists in full at
+any point in its lifetime, persists during this interval, and
+preserves the characteristics provided. In
+contrast, an activity is something that occurs, happens, unfolds, or
+develops through time. This
+distinction is similar to the distinction between 'continuant' and
+'occurrent' in logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>].</p>
+
+
+</section>
+<section id="events">
+<h3><span class="secno">2.2 </span>Events</h3>
+
+<p> Although time is important for provenance, provenance can be used
+in many different contexts within individual systems and across the
+Web. Different systems may use different clocks which may not be
+precisely synchronized, so when provenance statements are combined by
+different systems, an application may not be able to align the times involved to a
+single global timeline. Hence, PROV is designed to minimize
+assumptions about time. Instead, PROV talks about (identified)
+events. </p>
+
+<p>The PROV data model is implicitly based on a notion of <dfn id="dfn-event">instantaneous event</dfn>s (or just <a title="instantaneous event" href="#dfn-event" class="internalDFN">event</a>s), that mark
+transitions in the world. Events include generation, usage, or
+invalidation of entities, as well as start or end 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 [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>].
+Thus, events help justify <i>inferences</i> on provenance as well as
+<i>validity</i> constraints indicating when provenance is
+ self-consistent.
+
+
+
+</p><p>Five kinds of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous
+events</a> are used in PROV. The <strong>activity start</strong>
+and <strong>activity end</strong> events delimit the beginning and the
+end of activities, respectively. The
+<strong>entity generation</strong>, <strong>entity usage</strong>, and <strong>entity
+invalidation</strong> events apply to entities, and the generation and
+invalidation events delimit the <a href="#lifetime" class="internalDFN">lifetime</a> of an entity. More
+precisely:
+</p>
+
+<p>An <dfn id="dfn-start-event">activity start event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity starts.</p>
+
+<p>An <dfn id="dfn-end-event">activity end event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity ends.</p>
+
+<p>An <dfn id="dfn-generation-event">entity generation event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the final instant of an entity's creation timespan, after which
+it is available for use. The entity did not exist before this event.</p>
+
+
+<p>An <dfn id="dfn-usage-event">entity usage event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the first instant of
+an entity's consumption timespan by an activity. The described usage
+had not started before this instant, although the activity could
+potentially have used the same entity at a different time.</p>
+
+
+<p>An <dfn id="dfn-invalidation-event">entity invalidation event</dfn>
+is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that
+marks the initial instant of the destruction, invalidation, or
+cessation of an entity, after which the entity is no longer available
+for use. The entity no longer exists after this event.</p>
+
+</section>
+
+<section id="typing-section">
+<h3><span class="secno">2.3 </span>Types</h3>
+
+<p> As set out in other specifications, the identifiers used in PROV
+documents have associated type information. An identifier can have
+more than one type, reflecting subtyping or allowed overlap between
+types, and so we define a set of types of each identifier, <span class="name">typeOf(id)</span>. Some types are, however,
+required not to overlap (for example, no identifier can describe both
+an entity and an activity).
+In addition, an identifier cannot be used to identify both an object
+(that is, an entity, activity or agent) and a property (that is, a
+named event such as usage, generation, or a relationship such as
+attribution.)
+This specification includes <a href="#type-constraints">disjointness and typing constraints</a> that
+check these requirements. Here, we
+summarize the type constraints in <a href="#typing-table">Table 1</a>.
+</p>
+
+<div id="typing-table-fig">
+ <table id="typing-table" border="1" class="thinborder" style="margin-left: auto; margin-right: auto; border-color: black;">
+<caption id="typing-table-caption">Table 1: Summary of Typing Constraints</caption>
+ <tbody><tr>
+ <th>In relation...</th>
+ <th>identifier</th>
+ <th>has type(s)...</th>
+ </tr>
+
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+ <tr style="text-align: center; ">
+ <td class="name">entity(e,attrs)</td>
+ <td class="name" style="text-align: center; ">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">activity(a,t1,t2,attrs)</td>
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">agent(ag,attrs)</td>
+ <td class="name">ag</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">used(id; a,e,t,attrs)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasGeneratedBy(id; e,a,t,attrs)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasInformedBy(id; a2,a1,attrs)</td>
+ <td class="name">a2</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a1</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasStartedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">a2</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a1</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasEndedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">a2</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a1</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasInvalidatedBy(id; e,a,t,attrs)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)</td>
+ <td class="name">e2</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e1</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasAttributedTo(id; e,ag,attr)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">ag</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasAssociatedWith(id; a,ag,pl,attrs)</td>
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">ag</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">pl</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">actedOnBehalfOf(id; ag2,ag1,a,attrs)</td>
+ <td class="name">ag2</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">ag1</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">alternateOf(e1,e2)</td>
+ <td class="name">e1</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e2</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">specializationOf(e1,e2)</td>
+ <td class="name">e1</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e2</td>
+ <td class="name">'entity'</td>
+ </tr>
+<!--
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">mentionOf(e1,e2,b)</td>
+ <td class="name">e1</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e2</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">b</td>
+ <td class="name">'entity'</td>
+ </tr>
+-->
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">hadMember(c,e)</td>
+ <td class="name">c</td>
+ <td class="name">'entity'<br> 'prov:Collection'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">entity(c,[prov:type='prov:EmptyCollection,...])</td>
+ <td class="name">c</td>
+ <td class="name">'entity'<br> 'prov:Collection' <br> 'prov:EmptyCollection'</td>
+ </tr>
+ </tbody></table>
+ </div>
+
+</section>
+<section id="validation-process-overview-1">
+<h3><span class="secno">2.4 </span>Validation Process Overview</h3>
+
+
+ <p>
+ This section collects common concepts and operations that are used
+ throughout the specification, and relates them to background
+ terminology and ideas from logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>], constraint programming
+ [<cite><a class="bibref" href="#bib-CHR">CHR</a></cite>], and database constraints [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]. This section
+ does not attempt to provide a complete introduction to these topics,
+ but it is provided in order to aid readers familiar with one or more
+ of these topics in understanding the specification, and to clarify
+ some of the motivations for choices in the specification to all
+ readers.
+ </p>
+
+ <p>As discussed below, the definitions, inferences and constraints
+can be viewed as pure logical assertions that could be checked in a
+variety of ways. The rest of this document specifies validity and
+equivalence procedurally, that is, in terms of a reference
+implementation based on normalization. Although both declarative and
+procedural specification techniques have advantages, a purely
+declarative specification offers much less guidance for
+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
+be used as a starting point for other implementation strategies. </p>
+
+
+
+ <h3 id="constants-variables-and-placeholders">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/prov-n/#prod-QUALIFIED_NAME">qualified names</a> which can be mapped to URIs [<cite><a class="bibref" href="#bib-RFC3987">RFC3987</a></cite>].
+ However, in order to specify
+ constraints over PROV instances, we also need <em>variables</em>
+ that represent unknown identifiers, literals, or placeholders.
+ These variables are similar to those in first-order
+ logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>]. A variable is a symbol that can be replaced by
+ other symbols, including either other variables or constant
+ identifiers, literals, or placeholders. In a few special cases, we
+ also use variables for unknown attribute lists.
+ To help distinguish identifiers and variables, we also term the former 'constant identifiers' to highlight their non-variable nature.
+ </p>
+
+ <p>Several definitions and inferences conclude by saying that some
+ objects exist such that some other formulas hold. Such an inference
+ introduces fresh <a>existential variable</a>s into the instance. An
+ existential variable denotes a fixed object that exists, but its
+ exact identity is unknown. Existential variables can stand for
+ unknown identifiers or literal values only; we do not allow
+ existential variables that stand for unknown attribute lists. </p>
+
+ <p>In particular, many
+ occurrences of the placeholder symbol <span class="name">-</span> stand for unknown
+ objects; these are handled by expanding them to existential
+ variables. Some placeholders, however, indicate the absence of an
+ object, rather than an unknown object. In other words, the
+ placeholder is overloaded, with different meanings in different
+ places.
+ </p>
+ <p>An expression is called a <em>term</em> if it is either a
+ constant identifier, literal, placeholder, or variable. We write
+ <span class="math">t</span> to denote an arbitrary term.
+</p>
+
+
+ <h4 id="substitution-1">Substitution</h4><p><em>This section is non-normative.</em></p>
+<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
+ <span class="math">S = [x<sub>1</sub> = t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span>
+ can be <em>applied</em> to a term by replacing occurrences of
+<span class="math">x_i</span> with <span class="math">t_i</span>.
+</p>
+<!--
+as follows.
+<ol><li>
+ If the term is a variable <span class="math">x<sub>i</sub></span>, one of the variables in the
+ domain of <span class="math">S</span>, then <span class="math">S(x<sub>i</sub>) = t<sub>i</sub></span>.
+ </li>
+ <li>If the term is a constant identifier or literal <span
+ class="math">c</span>, then <span class="math">S(c) = c</span>.
+ </li>
+ </ol>
+-->
+ <p>
+ In addition, a substitution can be applied to an atomic formula
+ (PROV statement) <span class="math">p(t<sub>1</sub>,...,t<sub>n</sub>)</span> by applying it to each term,
+ that is, <span class="math">S(p(t<sub>1</sub>,...,t<sub>n</sub>)) = p(S(t<sub>1</sub>),...,S(t<sub>n</sub>))</span>. Likewise, a
+ substitution <span class="math">S</span> can be applied to an instance <span class="math">I</span> by applying
+ it to each atomic formula (PROV statement) in <span class="math">I</span>, that is, <span class="math">S(I)
+ = {S(A) | A ∈ I}</span>.
+</p>
+
+
+
+
+
+ <h4 id="formulas">Formulas</h4>
+ <p>
+ For the purpose of constraint checking, we view PROV statements
+ (possibly involving existential variables) as
+ <dfn id="dfn-formulas">formulas</dfn>. An instance is analogous to a "theory" in
+ logic, that is, a set of formulas all thought to describe the same
+ situation. The set can also be thought of a single, large formula:
+ the conjunction of all of the atomic formulas.
+ </p>
+<p>The atomic constraints considered in this specification can be
+ viewed as atomic formulas:</p>
+<ul>
+ <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>
+ </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>.
+ </li>
+ <li>Impossibility constraints employ the conclusion <span class="name">INVALID</span>,
+ which is equivalent to the logical constant <span class="math">False</span>. </li>
+ </ul>
+ <p> Similarly, the definitions, inferences, and constraint rules in this
+ specification can also be viewed as logical formulas, built up out
+ of atomic formulas, logical connectives "and" (∧), "implies" (⇒),
+ and quantifiers "for all" (∀) and "there exists" (∃). For more
+ 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>
+ 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
+ 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
+ <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
+ <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>
+ <p>
+ In logic, a formula's meaning is defined by saying when it is
+ <em>satisfied</em>. We can view
+ definitions, inferences, and constraints as being satisfied or not
+ satisfied in a PROV instance, augmented with information about the constraints.
+ </p>
+ <ol>
+ <li>A logical equivalence as used in a definition is satisfied
+ when the 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> holds, that is, for any substitution of the
+ variables <span class="math">x<sub>1</sub>,....,x<sub>n</sub></span>, formula <span class="math">A</span> and
+ formula <span class="math">∃
+ y<sub>1</sub>...y<sub>m</sub>. B<sub>1</sub> ∧ ... ∧
+ 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">∀
+ 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
+ the variables <span class="math">x<sub>1</sub>,....,x<sub>n</sub></span>, if <span class="math">A<sub>1</sub> ∧ ... ∧
+ A<sub>p</sub></span> is true, then
+ for some further substitution of terms for variables <span class="math">
+ y<sub>1</sub>...y<sub>m</sub></span>, formula <span class="math">B<sub>1</sub> ∧ ... ∧
+ B<sub>k</sub></span> is also true.</li>
+ <li>A uniqueness, ordering, or typing constraint is satisfied when
+ its associated formula <span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ C</span> holds, that is, for any substitution of
+ the variables <span class="math">x<sub>1</sub>,....,x<sub>n</sub></span>, if <span class="math">A<sub>1</sub> ∧ ... ∧
+ A<sub>p</sub></span> is true, then <span class="math">C</span> is
+ also true.</li>
+ <li>An impossibility constraint is satisfied when the formula
+ <span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒
+ False</span> holds. This is logically equivalent to <span class="math">∄
+ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span>, that is, there exists no
+ 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>
+
+ <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
+ existential variable with another term. If so, the result is such a
+ substitution; otherwise, the result is failure. Unification is an
+ essential concept in logic programming and automated reasoning,
+where terms can involve variables, constants and function symbols. In PROV,
+ by comparison, unification only needs to deal with variables,
+ constants and literals.
+</p>
+<p>
+Unifying two terms <span class="math">t,t'</span> results in either substitution <span class="math">S</span>
+ such that <span class="math">S(t) = S(t')</span>, or failure indicating that there is no
+ substitution that can be applied to both <span class="math">t</span> and <span class="math">t'</span> to make
+ them equal. Unification is also used to define an operation on PROV
+ statements called <em>merging</em>. Merging takes two statements
+ that have equal identifiers, unifies their corresponding term
+ arguments, and combines their attribute lists.
+</p>
+
+
+
+ <h4 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h4>
+<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
+ instance that does satisfy the formula. Definitions, inferences,
+ and uniqueness constraints can be applied to instances:
+</p>
+ <ul>
+ <li>
+ A definition of the form <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>
+ can be applied by searching for any occurrences of <span class="math">A</span> in the instance and adding <span class="math"> B<sub>1</sub>, ..., B<sub>k</sub></span>, generating fresh existential
+ variables <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>, and conversely, whenever there is an
+ occurrence of <span class="math"> B<sub>1</sub>, ..., B<sub>k</sub></span>, adding
+ <span class="math">A</span>.
+ In our setting, the defined formulas <span class="math">A</span> are never used in other
+ formulas, so it is sufficient to replace all occurrences of
+ <span class="math">A</span> with their definitions. The formula <span class="math">A</span> is then redundant, and can be
+ removed from the instance.
+</li>
+<li>An inference of the form <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> 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,
+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
+ variables <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>.
+</li>
+<li>A uniqueness constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ t
+= t'</span> can be
+ applied by searching for an occurrence <span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> in the instance, and
+ if one is found, unifying the terms <span class="math">t</span> and
+<span class="math">t'</span>. If successful, the resulting
+substitution is applied to the instance; otherwise, the application
+of the uniqueness constraint fails. </li>
+<li>A key constraint can similarly be applied by searching for
+different occurrences of a statement with the same identifier, unifying the
+corresponding parameters of the statements, and concatenating their
+attribute lists, to form a single statement. The substitutions obtained by unification are applied to
+the merged statement and the rest of the instance.
+</li>
+ </ul>
+
+ <p>As noted above, uniqueness or key constraint
+ application can <em>fail</em>, if a required unification or merging step fails. Failure of constraint
+ application means that there is no way to add information to the
+ instance to satisfy the constraint, which in turn implies that the
+ instance is <em>invalid</em>.
+ </p>
+ <p>
+ The process of applying definitions, inferences, and constraints
+ to a PROV instance until all of them are satisfied is similar to
+ what is sometimes
+ called <em>chasing</em> [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>] or <em>saturation</em>
+ [<cite><a class="bibref" href="#bib-CHR">CHR</a></cite>]. We call this process <em>normalization</em>.
+ </p>
+ <p>
+ Although this specification outlines one particular way of
+ performing inferences and checking constraints, based on
+ normalization, implementations can use any other equivalent
+ algorithm. The logical formulas corresponding to the definitions,
+ inferences, and constraints outlined above (and further elaborated
+ in [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>]) provides an equivalent specification, and any
+ implementation that correctly checks validity and equivalence (whether it performs normalization or not) complies
+ with this specification.
+ </p>
+
+
+ <h4 id="termination-1">Termination</h4>
+ <p>
+ In general, applying sets of logical formulas of the above
+ definition, inference, and constraint forms is not guaranteed to
+ terminate. A simple example is the inference <span class="math">R(x,y) ⇒ ∃z. R(x,z)
+ ∧R(z,y)</span>, which can be applied to <span class="math">{R(a,b)}</span> to generate an
+ infinite sequence of larger and larger instances. To ensure that
+ normalization, validity, and equivalence are decidable, we require
+ that normalization terminates. There is a great deal of work on termination of the chase in
+ databases, or of sets of constraint handling rules. The termination
+ of the notion of normalization defined in this specification is
+ guaranteed because the definitions, inferences and uniqueness/key
+ constraints correspond to a <em>weakly acyclic</em> set of
+ tuple-generating and equality-generating dependencies, in the
+ terminology of [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]. The termination of the remaining
+ ordering, typing, and impossibility constraints is easy to show. <a href="#termination">Appendix
+ A</a> gives a proof that the definitions, inferences, and uniqueness
+ and key constraints are weakly acyclic and therefore terminating.
+ </p>
+ <p>
+ There is an important subtlety that is essential to guarantee
+ termination. This specification draws a distinction between knowing
+ that an identifier has type <span class="name">'entity'</span>, <span class="name">'activity'</span>, or <span class="name">'agent'</span>, and having
+ an explicit <span class="name">entity(id)</span>, <span class="name">activity(id)</span>, or <span class="name">agent(id)</span> statement in the instance.
+ For example, focusing on entity statements, we can infer <span class="name">'entity' ∈ typeOf(id)</span> if <span class="name">entity(id)</span> holds in the instance. In contrast, if we only know
+ that <span class="name">'entity' ∈ typeOf(id)</span>, this does not imply that <span class="name">entity(id)</span>
+ holds.
+ </p>
+ <p>
+ This distinction (for both entities and activities) is essential to
+ ensure termination of the inferences, because we allow inferring
+ that a declared <span class="name">entity(id,attrs)</span> has a generation
+ and invalidation event, using
+ <a class="rule-text" href="#entity-generation-invalidation-inference_text"><span>Inference 7 (entity-generation-invalidation-inference)</span></a>.
+ Likewise, for activities, we allow inferring that a declared <span class="name">activity(id,t1,t2,attrs)</span> has a generation
+ and invalidation event, using
+ <a class="rule-text" href="#activity-start-end-inference_text"><span>Inference 8 (activity-start-end-inference)</span></a>. These
+ inferences do not apply to identifiers whose types are known, but for
+ which there is not an explicit entity or activity statement.
+If we strengthened the type
+ inference constraints to add new entity or activity statements for
+ the entities and activities involved in generating or starting other
+ declared entities or activities, then we could keep generating new entities and
+ activities in an unbounded chain into the past (as in the "chicken
+ and egg" paradox). The
+ design adopted here requires that instances explicitly declare the
+ entities and activities that are relevant for validity checking, and only
+ these can be inferred to have invalidation/generation and start/end events. This inference
+ is not supported for identifiers
+that are indirectly referenced in other relations and therefore have
+ type <span class="name">'entity'</span> or <span class="name">'activity'</span>.
+ </p>
+
+
+<div style="text-align: center;">
+<span class="figure" id="fig-figure-1-overview-of-the-validation-process">
+<img src="images/constraints/prov-c.graffle.svg/overview.svg" alt="validation process overview">
+<br>
+<span class="figcaption" id="validation-process-overview">Figure 1<sup><a class="internalDFN" href="#validation-process-overview"><span class="diamond"> ◊:</span></a></sup> Overview of the Validation Process</span>
+</span> <!-- <b>new Figure 1:</b> -->
+</div>
+
+
+ <h4 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h4>
+ <p>
+ The ordering, typing, and impossibility constraints are checked
+ rather than applied. This means that they do not generate new
+ formulas expressible in PROV, but they do generate basic constraints
+ that might or might not be consistent with each other. Checking
+ such constraints follows a saturation strategy similar to that for normalization:
+ </p>
+ <ol>
+ <li><p>
+ For ordering constraints, we check by generating all of the
+ precedes and strictly-precedes relationships specified by the rules. These can be thought
+ of as a directed graph whose nodes are terms, and whose edges are
+ precedes or strictly-precedes relationships.
+ An ordering constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒
+precedes(t,t')</span> can be applied by searching for occurrences of
+<span class="math"> A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> and for each such match
+adding the atomic formula <span class="math">precedes(t,t')</span> to
+ the instance, and similarly for strictly-precedes constraints. After all such constraints have been checked, and the
+ resulting edges added to the graph, the ordering constraints are
+ violated if there is a cycle in the graph that includes a
+ strictly-precedes edge, and satisfied otherwise.
+ </p>
+</li>
+<li><p>For typing constraints, we check by constructing a function
+ <span class="math">typeOf(id)</span> mapping identifiers to sets of possible types. We
+ start with a function mapping each identifier to the empty set,
+ reflecting no constraints on the identifiers' types. A typing
+ constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ 'type' ∈ typeOf(id)
+</span> is checked by adjusting the
+ function by adding <span class="name">'type'</span> to <span class="math">typeOf(id)</span> for each conclusion
+ <span class="name">'type' ∈ typeOf(id)</span> of the rule. Typing constraints with
+ multiple conclusions are handled analogously. Once all constraints
+ have been checked in all possible ways, we check that the
+ disjointness constraints hold of the resulting <span class="math">typeOf</span> function.
+ (These are essentially impossibility constraints).
+</p>
+ </li>
+ <li><p>For impossibility constraints, we check by searching for the
+ forbidden pattern that the impossibility constraint describes. Any
+ match of this pattern leads to failure of the constraint checking process.
+An impossibility constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒
+False</span> can be applied by searching for occurrences of
+<span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> in the instance, and if any
+such occurrence is found, signaling failure.</p>
+ </li>
+ </ol>
+ <p>
+ A normalized instance that passes all of the ordering, typing,
+ and impossibility constraint checks
+ is called <a href="#dfn-valid" class="internalDFN">valid</a>. Validity can be, but is not required to be,
+ checked by normalizing and then checking constraints. Any other
+ algorithm that provides equivalent behavior (that is, accepts the
+ same valid instances and rejects the same invalid instances) is allowed.
+ In particular, the checked constraints and the
+ applied definitions, inferences and uniqueness constraints do not
+ interfere with one another, so it is also possible to mix checking
+ and application. This may be desirable in order to detect
+ invalidity more quickly.
+ </p>
+
+
+
+ <h4 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h4>
+ <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
+ logic, if we consider normalized PROV instances with existential
+ variables to represent sets of possible situations, then two normal
+ forms may describe the same situation but differ in inessential
+ details such as the order of statements or of elements of
+ attribute-value lists. To remedy this, we can easily consider
+ instances to be equivalent up to reordering of attributes. However,
+ instances can also be equivalent if they differ only in choice of
+ names of existential variables. Because of this, the appropriate
+ notion of equivalence of normal forms is <em>isomorphism</em>. Two
+ instances <span class="math">I<sub>1</sub></span> and <span class="math">I<sub>2</sub></span> are <em>isomorphic</em> if there is an invertible
+ substitution <span class="math">S</span> mapping existential variables to existential variables such that <span class="math">S(I<sub>1</sub>) = I<sub>2</sub></span>.
+<!--
+ This is similar to the notion of equivalence used in [[RDF]], where
+ blank nodes play an analogous role to existential variables.
+ -->
+ </p>
+
+<p>Equivalence can be checked by normalizing instances, checking that
+ both instances are valid, then
+ testing whether the two normal forms are isomorphic. (It is
+ technically possible for two invalid normal forms to be isomorphic,
+ but to be considered equivalent, the two instances must also be
+ valid.)
+As with validity, the algorithm suggested by this specification is
+ just one of many possible ways to implement equivalence checking; it
+ is not required that implementations compute normal forms
+ explicitly, only that their determinations of equivalence match
+ those obtained by the algorithm in this specification.
+ </p>
+
+<p>Equivalence is only explicitly specified for
+valid instances (whose normal forms exist and are unique up to
+isomorphism). Implementations may test equivalences involving valid
+and invalid documents. This specification does not constrain the
+behavior of equivalence checking involving invalid instances, provided
+that:
+</p>
+<ul>
+ <li>instance equivalence is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-symmetric" class="internalDFN">symmetric</a> and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a> on all instances</li>
+ <li> no valid instance is equivalent to an invalid instance.</li>
+ </ul>
+<p>
+Because of the second constraint, equivalence is essentially the union
+ of two equivalence relations on the disjoint sets of valid and
+ invalid instances.
+ There are two simple implementations of equivalence for invalid
+ documents that are correct:</p>
+ <ol>
+ <li>each invalid instance is equivalent only to itself</li>
+ <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>
+
+<p>PROV documents can contain multiple instances: a <a>toplevel
+instance</a>, and
+zero or more additional, named instances called <a>bundle</a>s. For the purpose
+of inference and constraint checking, these instances are treated independently. That is,
+a PROV document is valid provided that each instance in it is valid
+and the names of its bundles are distinct. In other words, there are
+no validity constraints that need to be checked across the different
+instances in a PROV document; the contents of one instance in a
+multi-instance PROV document cannot affect the validity of another instance.
+Similarly, a PROV document is
+equivalent to another if their toplevel instances are equivalent, they
+have the same number of bundles with the same names, and the instances
+of their corresponding bundles are equivalent.
+<!--Analogously to blank nodes in
+[[RDF]],-->
+The scope of an existential variable in PROV is delimited at the instance
+level, so existential variables with the same name occurring in
+different instances do not necessarily denote the same term. This
+is a consequence of the fact that the instances of two equivalent
+documents only need to be pairwise isomorphic; this is a weaker
+property than requiring that there be a single isomorphism that works
+for all of the corresponding instances.
+</p>
+</section>
+
+<section id="summary-of-inferences-and-constraints">
+<h3><span class="secno">2.5 </span>Summary of inferences and constraints</h3>
+
+<p><a href="">Table 2</a> summarizes the inferences, and
+constraints specified in this document, broken down by component and
+type or relation involved.
+</p>
+
+<!--
+<div class="note">Table: work in progress; these entries might change when the document is updated.</div>
+-->
+
+<div id="prov-constraints-fig" style="text-align: left;">
+<table class="thinborder" style="margin-left: auto; margin-right: auto; border-color: black;">
+<caption id="prov-constraints">Table 2: Summary of inferences and constraints for PROV Types and Relations</caption>
+<tbody><tr><td><a><b>Type or Relation Name</b></a></td><td><b>
+ Inferences and Constraints</b></td><td><b>Component</b></td></tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+
+<tr class="component1-color">
+ <td class="essential"><a>Entity</a></td>
+ <td><a class="rule-text" href="#entity-generation-invalidation-inference_text"><span>Inference 7 (entity-generation-invalidation-inference)</span></a><br>
+ <a class="rule-text" href="#specialization-attributes-inference_text"><span>Inference 21 (specialization-attributes-inference)</span></a><br>
+ <a class="rule-text" href="#key-object_text"><span>Constraint 22 (key-object)</span></a><br>
+ <a class="rule-text" href="#impossible-object-property-overlap_text"><span>Constraint 54 (impossible-object-property-overlap)</span></a><br>
+ <a class="rule-text" href="#entity-activity-disjoint_text"><span>Constraint 55 (entity-activity-disjoint)</span></a><br>
+ </td>
+ <td rowspan="8" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component1" title="Component 1: Entities/Activities">1</a></td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Activity</a></td>
+ <td><a class="rule-text" href="#activity-start-end-inference_text"><span>Inference 8 (activity-start-end-inference)</span></a><br>
+ <a class="rule-text" href="#key-object_text"><span>Constraint 22 (key-object)</span></a><br>
+ <a class="rule-text" href="#unique-startTime_text"><span>Constraint 28 (unique-startTime)</span></a><br>
+ <a class="rule-text" href="#unique-endTime_text"><span>Constraint 29 (unique-endTime)</span></a><br>
+ <a class="rule-text" href="#impossible-object-property-overlap_text"><span>Constraint 54 (impossible-object-property-overlap)</span></a><br>
+ <a class="rule-text" href="#entity-activity-disjoint_text"><span>Constraint 55 (entity-activity-disjoint)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Generation</a></td>
+ <td><a class="rule-text" href="#generation-use-communication-inference_text"><span>Inference 6 (generation-use-communication-inference)</span></a><br>
+<!-- <a class="rule-text" href="#derivation-use-inference"><span>TBD</span></a><br>-->
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-generation_text"><span>Constraint 24 (unique-generation)</span></a><br>
+ <a class="rule-text" href="#generation-within-activity_text"><span>Constraint 34 (generation-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-invalidation_text"><span>Constraint 36 (generation-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-usage_text"><span>Constraint 37 (generation-precedes-usage)</span></a><br>
+ <a class="rule-text" href="#generation-generation-ordering_text"><span>Constraint 39 (generation-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#derivation-usage-generation-ordering_text"><span>Constraint 41 (derivation-usage-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#derivation-generation-generation-ordering_text"><span>Constraint 42 (derivation-generation-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasStartedBy-ordering_text"><span>Constraint 43 (wasStartedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasEndedBy-ordering_text"><span>Constraint 44 (wasEndedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#specialization-generation-ordering_text"><span>Constraint 45 (specialization-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint 47 (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAttributedTo-ordering_text"><span>Constraint 48 (wasAttributedTo-ordering)</span></a><br>
+ <a class="rule-text" href="#actedOnBehalfOf-ordering_text"><span>Constraint 49 (actedOnBehalfOf-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Usage</a></td>
+ <td><a class="rule-text" href="#generation-use-communication-inference_text"><span>Inference 6 (generation-use-communication-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#usage-within-activity_text"><span>Constraint 33 (usage-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-usage_text"><span>Constraint 37 (generation-precedes-usage)</span></a><br>
+ <a class="rule-text" href="#usage-precedes-invalidation_text"><span>Constraint 38 (usage-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#derivation-usage-generation-ordering_text"><span>Constraint 41 (derivation-usage-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Communication</a></td>
+ <td><a class="rule-text" href="#communication-generation-use-inference_text"><span>Inference 5 (communication-generation-use-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#wasInformedBy-ordering_text"><span>Constraint 35 (wasInformedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Start</a></td>
+ <td><a class="rule-text" href="#wasStartedBy-inference_text"><span>Inference 9 (wasStartedBy-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-wasStartedBy_text"><span>Constraint 26 (unique-wasStartedBy)</span></a><br>
+ <a class="rule-text" href="#unique-startTime_text"><span>Constraint 28 (unique-startTime)</span></a><br>
+ <a class="rule-text" href="#start-precedes-end_text"><span>Constraint 30 (start-precedes-end)</span></a><br>
+ <a class="rule-text" href="#usage-within-activity_text"><span>Constraint 33 (usage-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-within-activity_text"><span>Constraint 34 (generation-within-activity)</span></a><br>
+ <a class="rule-text" href="#wasInformedBy-ordering_text"><span>Constraint 35 (wasInformedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#start-start-ordering_text"><span>Constraint 31 (start-start-ordering)</span></a><br>
+ <a class="rule-text" href="#wasStartedBy-ordering_text"><span>Constraint 43 (wasStartedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint 47 (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>End</a></td>
+ <td><a class="rule-text" href="#wasEndedBy-inference_text"><span>Inference 10 (wasEndedBy-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-wasEndedBy_text"><span>Constraint 27 (unique-wasEndedBy)</span></a><br>
+ <a class="rule-text" href="#unique-endTime_text"><span>Constraint 29 (unique-endTime)</span></a><br>
+ <a class="rule-text" href="#start-precedes-end_text"><span>Constraint 30 (start-precedes-end)</span></a><br>
+ <a class="rule-text" href="#usage-within-activity_text"><span>Constraint 33 (usage-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-within-activity_text"><span>Constraint 34 (generation-within-activity)</span></a><br>
+ <a class="rule-text" href="#wasInformedBy-ordering_text"><span>Constraint 35 (wasInformedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#end-end-ordering_text"><span>Constraint 32 (end-end-ordering)</span></a><br>
+ <a class="rule-text" href="#wasEndedBy-ordering_text"><span>Constraint 44 (wasEndedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint 47 (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Invalidation</a></td>
+ <td><a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-invalidation_text"><span>Constraint 25 (unique-invalidation)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-invalidation_text"><span>Constraint 36 (generation-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#usage-precedes-invalidation_text"><span>Constraint 38 (usage-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#invalidation-invalidation-ordering_text"><span>Constraint 40 (invalidation-invalidation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasStartedBy-ordering_text"><span>Constraint 43 (wasStartedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasEndedBy-ordering_text"><span>Constraint 44 (wasEndedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#specialization-invalidation-ordering_text"><span>Constraint 46 (specialization-invalidation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint 47 (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAttributedTo-ordering_text"><span>Constraint 48 (wasAttributedTo-ordering)</span></a><br>
+ <a class="rule-text" href="#actedOnBehalfOf-ordering_text"><span>Constraint 49 (actedOnBehalfOf-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+
+<tr class="component2-color">
+ <td class="essential"><a>Derivation</a></td>
+ <td><a class="rule-text" href="#derivation-generation-use-inference_text"><span>Inference 11 (derivation-generation-use-inference)</span></a><br>
+<!-- <a class="rule-text" href="#derivation-use-inference"><span>TBD</span></a><br>-->
+<!-- <a class="rule-text" href="#specific-derivation-inference"><span>TBD</span></a><br>-->
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#derivation-usage-generation-ordering_text"><span>Constraint 41 (derivation-usage-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#derivation-generation-generation-ordering_text"><span>Constraint 42 (derivation-generation-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+ <td rowspan="5" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component2" title="Component 2: Derivations">2</a></td>
+</tr>
+<tr class="component2-color">
+ <td class="provType"><a>Revision</a></td>
+ <td><a class="rule-text" href="#revision-is-alternate-inference_text"><span>Inference 12 (revision-is-alternate-inference)</span></a><br></td>
+</tr>
+<tr class="component2-color">
+ <td class="provType"><a>Quotation</a></td>
+ <td>No specific constraints</td>
+</tr>
+<tr class="component2-color">
+ <td class="provType"><a>Primary Source</a></td>
+ <td>No specific constraints</td>
+</tr>
+<tr class="component2-color">
+ <td><a class="essential">Influence</a></td>
+ <td>No specific constraints</td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component3-color" style="border-collapse: collapse; ">
+ <td class="essential"><a>Agent</a></td>
+ <td><a class="rule-text" href="#key-object_text"><span>Constraint 22 (key-object)</span></a><br>
+ <a class="rule-text" href="#impossible-object-property-overlap_text"><span>Constraint 54 (impossible-object-property-overlap)</span></a><br>
+ </td>
+ <td rowspan="5" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component3" title="Component 3: Agents/Responsibility">3</a></td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Attribution</a></td>
+ <td><a class="rule-text" href="#attribution-inference_text"><span>Inference 13 (attribution-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#wasAttributedTo-ordering_text"><span>Constraint 48 (wasAttributedTo-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Association</a></td>
+ <td><a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint 47 (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Delegation</a></td>
+ <td><a class="rule-text" href="#delegation-inference_text"><span>Inference 14 (delegation-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ <a class="rule-text" href="#actedOnBehalfOf-ordering_text"><span>Constraint 49 (actedOnBehalfOf-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint 53 (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Influence</a></td>
+ <td><a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint 23 (key-properties)</span></a><br>
+ </td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component4-color">
+ <td><a title="bundle">Bundle constructor</a></td>
+ <td>No specific constraints; see <a href="#bundle-constraints" class="sectionRef sec-ref">section 7.2 Bundles and Documents</a></td>
+ <td rowspan="2" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component4" title="Component 4: Bundles">4</a></td>
+</tr>
+<tr class="component4-color">
+ <td class="provType"><a title="bundle">Bundle type</a></td>
+ <td> No specific constraints; see <a href="#bundle-constraints" class="sectionRef sec-ref">section 7.2 Bundles and Documents</a>
+ </td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component5-color">
+ <td><a>Alternate</a></td>
+ <td><a class="rule-text" href="#alternate-reflexive_text"><span>Inference 16 (alternate-reflexive)</span></a><br>
+ <a class="rule-text" href="#alternate-transitive_text"><span>Inference 17 (alternate-transitive)</span></a><br>
+ <a class="rule-text" href="#alternate-symmetric_text"><span>Inference 18 (alternate-symmetric)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+ <td rowspan="3" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component5" title="Component 5: Alternate Entities">5</a></td>
+</tr>
+<tr class="component5-color">
+ <td><a>Specialization</a></td>
+ <td><a class="rule-text" href="#specialization-transitive_text"><span>Inference 19 (specialization-transitive)</span></a><br>
+ <a class="rule-text" href="#specialization-alternate-inference_text"><span>Inference 20 (specialization-alternate-inference)</span></a><br>
+ <a class="rule-text" href="#specialization-attributes-inference_text"><span>Inference 21 (specialization-attributes-inference)</span></a><br>
+ <a class="rule-text" href="#specialization-generation-ordering_text"><span>Constraint 45 (specialization-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#specialization-invalidation-ordering_text"><span>Constraint 46 (specialization-invalidation-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-specialization-reflexive_text"><span>Constraint 52 (impossible-specialization-reflexive)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+<!--
+<tr class="component5-color">
+ <td><a>Mention</a></td>
+ <td><a class="rule-text" href="#mention-specialization-inference"><span>TBD</span></a><br>
+ <a class="rule-text" href="#unique-mention"><span>TBD</span></a><br>
+ <a class="rule-text" href="#typing"><span>TBD</span></a><br>
+ </td>
+</tr>
+-->
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component6-color">
+ <td><a>Collection</a></td>
+ <td> No specific constraints </td>
+ <td rowspan="2" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component6" title="Component 6: Collections">6</a></td>
+</tr>
+<tr class="component6-color">
+ <td><a>Membership</a></td>
+ <td> <a class="rule-text" href="#membership-empty-collection_text"><span>Constraint 56 (membership-empty-collection)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint 50 (typing)</span></a><br>
+ </td>
+</tr>
+</tbody></table>
+</div>
+
+
+</section>
+
+</section>
+
+<section id="compliance">
+<!--OddPage--><h2><span class="secno">3. </span>Compliance with this document</h2>
+
+<p>
+ For the purpose of compliance, the normative sections of this document
+ are <a href="#compliance" class="sectionRef sec-ref">section 3. Compliance with this document</a>,
+<a href="#concepts" class="sectionRef sec-ref">section 4. Basic concepts</a>,
+<a href="#inferences" class="sectionRef sec-ref">section 5. Definitions and Inferences</a>,
+<a href="#constraints" class="sectionRef sec-ref">section 6. Constraints</a>, and
+<a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section 7. Normalization, Validity, and Equivalence</a>.
+
+
+ To be compliant:
+ </p><ol><li>When processing provenance, an
+ application <em class="rfc2119" title="may">may</em> apply the inferences and definitions in <a href="#inferences" class="sectionRef sec-ref">section 5. Definitions and Inferences</a>.</li>
+ <li>If determining whether a PROV instance or document is <a href="#dfn-valid" class="internalDFN">valid</a>, an
+ application <em class="rfc2119" title="must">must</em> determine whether all of the
+ constraints of <a href="#constraints" class="sectionRef sec-ref">section 6. Constraints</a> are
+ satisfied on
+ the <a href="#dfn-normal-form" class="internalDFN">normal form</a> of the instance or document. </li>
+ <li> If producing provenance meant for other applications to
+ use, the application <em class="rfc2119" title="should">should</em> produce <a href="#dfn-valid" class="internalDFN">valid</a> provenance, as specified in <a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section 7. Normalization, Validity, and Equivalence</a>. </li>
+ <li>If determining whether two PROV instances or documents are
+ <a href="#dfn-equivalent" class="internalDFN">equivalent</a>, an application <em class="rfc2119" title="must">must</em> determine whether their
+ normal forms are equal, as specified in <a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section 7. Normalization, Validity, and Equivalence</a>.
+ </li></ol>
+
+ <p>This specification defines validity and equivalence procedurally
+ via reduction to normal forms. If checking validity or equivalence, the
+ results <em class="rfc2119" title="must">must</em> be the same as would be obtained by computing normal
+ forms as defined in this specification. Applications that explicitly compute
+ normal forms, following the implementation strategy suggested by
+ this specification, are by definition compliant. However,
+ applications can also comply by checking validity and equivalence in any
+ other way that yields the same answers without explicitly applying
+ definitions, inferences, and constraints or constructing normal forms.</p>
+
+ <p>
+ All figures are for illustration purposes
+ only. Information in tables is normative if it appears in a
+ normative section; specifically, <a href="#expandable-parameters-fig">Table 3</a> is normative. Text in appendices and
+in boxes labeled "Remark" is informative. Where there is any apparent
+ ambiguity between the descriptive text and the formal text in a
+ "definition", "inference" or "constraint" box, the formal text takes
+priority.
+ </p>
+
+
+
+</section>
+
+ <section id="concepts">
+ <!--OddPage--><h2><span class="secno">4. </span>Basic concepts</h2>
+
+ <p>This section specifies the key concepts of terms, statements, instances, substitution,
+ satisfaction, and unification, which have already been discussed in
+ <a href="#rationale">Section 2</a>.
+ </p>
+
+ <p>Many PROV relation statements have an identifier, identifying a
+ link between two or more related objects. Identifiers can sometimes
+ be omitted in [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>] notation. For the purpose of inference and
+ validity checking, we generate special identifiers called
+ <dfn id="dfn-variables">variables</dfn> denoting the unknown values.
+ Generally, identifiers occurring in constraints and inferences are
+ variables. Variables that are generated during inferences and
+ appear inside an instance are often called <dfn id="dfn-existential-variables">existential
+ variables</dfn>, because they are implicitly existentially quantified.
+</p>
+
+ <p> A <dfn id="term">PROV term</dfn> is a constant identifier
+ <span class="math">c</span>, a placeholder <span class="name">-</span>, a literal value,
+ or an existential variable <span class="math">x</span>. An
+ arbitrary PROV term is written <span class="math">t</span>.</p>
+
+ <p> A <dfn id="statement">PROV statement</dfn> is an expression of
+ the form <span class="math">p(t<sub>1</sub>,...,t<sub>n</sub>)</span> or <span class="math">p(id;t<sub>1</sub>,...,t<sub>n</sub>)</span> where
+ <span class="math">id,t<sub>1</sub>,...,t<sub>n</sub></span> are
+ PROV <a>term</a>s and <span class="math">p</span> is one of the
+ basic PROV relations. An arbitrary PROV statement is written <span class="math">A</span>.</p>
+
+<p> A <dfn id="instance">PROV instance</dfn> is a set of PROV
+ statements. Two instances are considered to be the same if they
+ contain the same statements, without regard to order or repetition.
+ An arbitrary PROV instance is written <span class="math">I</span>.
+</p>
+
+ <p>A <dfn id="substitution">substitution</dfn> <span class="math">S</span> is a mapping <span class="math">
+ [x<sub>1</sub>=t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span> associating existential variables
+ with terms. A substitution is <em>applied</em> to a term, statement
+ or instance by replacing all occurrences of each of the variables
+ <span class="math">x<sub>i</sub></span> with the corresponding <span class="math">t<sub>i</sub></span>. Specifically, if <span class="math">S =
+ [x<sub>1</sub>=t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span>
+ then the application of <span class="math">S</span> to a term, statement or instance, written <span class="math">S(t)</span>, <span class="math">S(A)</span> and
+ <span class="math">S(I)</span> respectively, is defined as follows:</p>
+<ul><li><span class="math">S(c) = c</span> if <span class="math">c</span> is a constant identifier.</li>
+<li><span class="math">S(x<sub>i</sub>) = t<sub>i</sub></span> if <span class="math">x<sub>i</sub></span> is one of the variables bound to a
+ term <span class="math">t<sub>i</sub></span> in <span class="math">S</span>.</li>
+<li><span class="math">S(x) = x</span> if <span class="math">x</span> is a variable not bound in <span class="math">S</span>.</li>
+<li><span class="math">S(p(t<sub>1</sub>,...,t<sub>n</sub>)) = p(S(t<sub>1</sub>),...,S(t<sub>n</sub>))</span>.</li>
+<li><span class="math">S(p(id;t<sub>1</sub>,...,t<sub>n</sub>)) = p(S(id);S(t<sub>1</sub>),...,S(t<sub>n</sub>))</span>.</li>
+<li><span class="math">S(I) = { S(A) | A ∈ I } </span> if <span class="math">I</span> is an instance.</li>
+</ul>
+
+ <p>Suppose <span class="math">A</span> is a statement and <span class="math">I</span> is an
+ instance and <span class="math">S</span> a substitution. We say that <span class="math">A</span> is
+ <dfn id="dfn-satisfied">satisfied</dfn> in <span class="math">I</span> by <span class="math">S</span> if <span class="math">S(A) ∈ I</span>. Likewise,
+ we say that a set of statements <span class="math">{A<sub>1</sub>,...,A<sub>n</sub>}</span> is satisfied in
+ <span class="math">I</span> if each <span class="math">A<sub>i</sub></span> is satisfied in <span class="math">I</span> by <span class="math">S</span>. Finally, we
+ say that a set of statements is <dfn id="dfn-satisfiable">satisfiable</dfn>
+ in <span class="math">I</span> if there is some substitution <span class="math">S</span> that satisfies the
+ statements in <span class="math">I</span>.
+</p>
+
+ <p> <dfn id="dfn-unification">Unification</dfn> is an operation that can be applied
+ to a pair of terms.
+ The result of unification is either a <dfn id="dfn-unifier">unifier</dfn>, that is, a substitution <span class="math">S</span> such that <span class="math">S(t)
+ = S(t')</span>, or failure, indicating
+ that there is no <a href="#dfn-unifier" class="internalDFN">unifier</a>. Unification of pairs of terms is defined as follows.</p>
+
+ <ul>
+ <li> If <span class="math">t</span> and <span class="math">t'</span> are constant identifiers or literal values
+ (including the placeholder <span class="name">-</span>), then
+ there are two cases. If <span class="math">t = t'</span> then their <a href="#dfn-unifier" class="internalDFN">unifier</a> is the
+ empty substitution, otherwise unification
+fails. </li>
+ <li> If <span class="math">x</span> is an existential variable
+ and
+ <span class="math">t'</span> is any term (identifier, constant,
+ placeholder <span class="name">-</span>, or
+ existential variable), then their
+ <a href="#dfn-unifier" class="internalDFN">unifier</a> is
+ <span class="math">[x=t']</span>. In the special case where
+ <span class="math">t'=x</span>, the <a href="#dfn-unifier" class="internalDFN">unifier</a> is the empty substitution.</li>
+ <li> If <span class="math">t</span> is any term (identifier, constant,
+ placeholder <span class="name">-</span>, or
+ existential variable) and
+ <span class="math">x'</span> is an existential variable, then their
+ <a href="#dfn-unifier" class="internalDFN">unifier</a> is the same as the <a href="#dfn-unifier" class="internalDFN">unifier</a> of <span class="math">x</span>
+ and <span class="math">t</span>.</li>
+ </ul>
+
+
+
+<div class="remark">Unification is analogous to unification in
+ logic programming and theorem proving, restricted to flat terms with
+constants and variables but no function symbols. No "occurs check" is needed because there are no
+ function symbols.</div>
+
+ <p>Two PROV instances <span class="math">I</span> and <span class="math">I'</span> are <dfn id="dfn-isomorphic">isomorphic</dfn> if
+ there exists an invertible substitution <span class="math">S</span> that maps each
+ variable of <span class="math">I</span> to a distinct variable of <span class="math">I'</span> and such that
+ <span class="math">S(I) = I'</span>.</p>
+
+
+</section>
+<section id="inferences">
+<!--OddPage--><h2><span class="secno">5. </span>Definitions and Inferences</h2>
+<p>
+This section describes <a title="definition" href="#definition" class="internalDFN">definitions</a> and <a title="inference" href="#inference" class="internalDFN">inferences</a> that <em class="rfc2119" title="may">may</em> be used on
+ provenance data, and that preserve <a>equivalence</a> on <a href="#dfn-valid" class="internalDFN">valid</a>
+PROV instances (as detailed in <a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section 7. Normalization, Validity, and Equivalence</a>).
+A <dfn id="definition">definition</dfn> is a rule that can be applied to
+ PROV instances to replace defined statements with other statements. An <dfn id="inference">inference</dfn> is a rule that can be applied
+ to PROV instances to add new PROV statements. A definition states that a
+ provenance statement is equivalent to some other statements, whereas
+ an inference only states one direction of an implication.
+</p>
+
+
+<p> Definitions have the following general form:</p>
+
+<div class="definition-example" id="definition-example"><div class="ruleTitle"><a class="internalDFN" href="#definition-example">Definition-example NNN (definition-example)</a></div>
+<p>
+ <span class="name">defined_stmt</span> <span class="conditional">IF AND ONLY IF</span>
+ there exists <span class="name">a<sub>1</sub></span>,..., <span class="name">a<sub>m</sub></span> such that <span class="name">defining_stmt<sub>1</sub></span> and ... and <span class="name">defining_stmt<sub>n</sub></span>.</p>
+ </div>
+
+ <p>
+ A definition can be applied to a PROV instance, since its <span class="name">defined_stmt</span> is defined in
+ terms of other statements. Applying a
+ definition to an instance means that if an occurrence of a defined
+ provenance statement <span class="name">defined_stmt</span>
+ can be found in a PROV instance, then we can remove it and add all of the statements
+<span class="name">defining_stmt<sub>1</sub></span> ... <span class="name">defining_stmt<sub>n</sub></span> to the instance, possibly after generating fresh
+ identifiers <span class="name">a<sub>1</sub></span>,...,<span class="name">a<sub>m</sub></span> for existential variables. In
+ other words, it is safe to replace
+ a defined statement with
+ its definition.
+</p>
+
+ <div class="remark">
+ We use definitions primarily to expand the compact, concrete
+ PROV-N syntax, including short forms and optional parameters, to the abstract syntax
+ implicitly used in PROV-DM.
+ </div>
+
+ <p> Inferences have the following general form:</p>
+<div class="inference-example" id="inference-example"><div class="ruleTitle"><a class="internalDFN" href="#inference-example">Inference-example NNN (inference-example)</a></div>
+<p>
+ <span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and
+<span class="name">hyp<sub>k</sub></span> <span class="conditional">THEN</span>
+ there exists <span class="name">a<sub>1</sub></span> and ... and <span class="name">a<sub>m</sub></span> such that <span class="name">concl<sub>1</sub></span> and ... and <span class="name">concl<sub>n</sub></span>.</p>
+ </div>
+
+<p> Inferences can be applied to PROV instances. Applying an inference to an instance means that if all of the provenance statements matching
+ <span class="name">hyp<sub>1</sub></span>... <span class="name">hyp<sub>k</sub></span>
+ can be found in the instance, then we check whether the conclusion
+ <span class="name">concl<sub>1</sub></span> ... <span class="name">concl<sub>n</sub></span> is <a href="#dfn-satisfied" class="internalDFN">satisfied</a> for some values
+ of existential variables. If so, application of the inference has
+ no effect on the instance. If not, then a copy the
+ conclusion should be added to the instance, after
+ generating fresh identifiers <span class="name">a<sub>1</sub></span>,...,<span class="name">a<sub>m</sub></span> for the existential variables. These fresh
+ identifiers might later be found to be equal to known identifiers;
+ they play a similar role in PROV constraints to existential
+ variables in logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>] or database theory
+ [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>].
+ <!--, or to blank nodes in [[!RDF]].-->
+ In general, omitted optional parameters to
+ [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>] statements, or explicit <span class="name">-</span>
+ markers, are placeholders for existentially quantified variables;
+ that is, they denote unknown values. There are a few exceptions to
+ this general rule, which are specified in <a class="rule-ref" href="#optional-placeholders"><span>Definition 4 (optional-placeholders)</span></a>.</p>
+
+<p> Definitions and inferences can be viewed as logical formulas;
+ similar formalisms are often used in rule-based reasoning [<cite><a class="bibref" href="#bib-CHR">CHR</a></cite>]
+ and in databases [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]. In particular, the identifiers
+ <span class="name">a<sub>1</sub></span> ... <span class="name">a<sub>n</sub></span>
+ should be viewed as existentially quantified variables, meaning that
+ through subsequent reasoning steps they may turn out to be equal to
+ other identifiers that are already known, or to other existentially
+ quantified variables.
+ <!--
+ Their treatment is analogous to that of blank
+ nodes in RDF.-->
+ In contrast, distinct URIs or literal values in PROV
+ are assumed to be distinct for the purpose of checking validity or
+ inferences. This issue is discussed in more detail under <a href="#uniqueness-constraints">Uniqueness Constraints</a>.
+ </p>
+
+<p>In a definition or inference, term symbols such as <span class="name">id</span>,
+ <span class="name">start</span>, <span class="name">end</span>, <span class="name">e</span>,
+ <span class="name">a</span>, <span class="name">attrs</span>,
+ are assumed to be variables unless otherwise specified. These variables are scoped at
+ the definition, inference, or constraint level, so the rule is equivalent to any one-for-one
+ renaming of the variable names. When several rules are
+ collected within a definition or inference
+ as an ordered list, the scope of the variables in each rule is at the level of list elements, and so reuse of
+ variable names in different rules does not affect the meaning.
+</p>
+<section id="optional-identifiers-and-attributes">
+ <h3><span class="secno">5.1 </span>Optional Identifiers and Attributes</h3>
+
+
+
+<p>
+<a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a>,
+<a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a>, and
+<a class="rule-ref" href="#definition-short-forms"><span>Definition 3 (definition-short-forms)</span></a>,
+ explain how to expand the compact forms of PROV-N notation into a
+ normal form. <a class="rule-ref" href="#optional-placeholders"><span>Definition 4 (optional-placeholders)</span></a> indicates when
+ other optional parameters can be replaced by <a href="#dfn-existential-variables" class="internalDFN">existential
+ variables</a>.
+</p>
+
+ <div class="definition" id="optional-identifiers"><div class="ruleTitle"><a class="internalDFN" href="#optional-identifiers">Definition 1 (optional-identifiers)</a></div>
+<p>For each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+<span class="name">wasInfluencedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasDerivedFrom</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>}, the following
+ definitional rules hold:</p>
+ <ol> <li>
+ <span class="name">r(a<sub>1</sub>,...,a<sub>n</sub>) </span> <span class="conditional">IF AND ONLY IF</span>
+ there exists <span class="name">id</span> such that <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>)</span>.</li>
+ <li> <span class="name">r(-; a<sub>1</sub>,...,a<sub>n</sub>) </span> <span class="conditional">IF AND ONLY IF</span>
+ there exists <span class="name">id</span> such that <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>)</span>.</li>
+ </ol>
+ </div>
+
+ <p>Likewise, many PROV-N statements allow for an optional attribute
+ list. If it is omitted, this is the same as specifying an empty
+ attribute list:</p>
+ <div class="definition" id="optional-attributes"><div class="ruleTitle"><a class="internalDFN" href="#optional-attributes">Definition 2 (optional-attributes)</a></div>
+<ol>
+ <li>
+ For each <span class="name">p</span> in {<span class="name">entity</span>, <span class="name">activity</span>,
+ <span class="name">agent</span>}, if <span class="name">a<sub>n</sub></span> is not an attribute
+ list parameter then the following definitional rule holds:
+ <p><span class="name">p(a<sub>1</sub>,...,a<sub>n</sub>)</span>
+ <span class="conditional">IF AND ONLY IF</span> <span class="name">p(a<sub>1</sub>,...,a<sub>n</sub>,[])</span>.
+ </p></li>
+ <li>
+ For each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidated</span>,
+<span class="name">wasInfluencedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasDerivedFrom</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>}, if <span class="name">a<sub>n</sub></span> is not an
+ attribute list parameter then the following definition holds:
+
+ <p> <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>)</span>
+ <span class="conditional">IF AND ONLY IF</span> <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>,[])</span>.</p></li></ol>
+ </div>
+
+
+ <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>.
+do not apply to <span class="name">alternateOf</span> and <span class="name">specializationOf</span>, which do not have identifiers and attributes.
+</p>
+ </div>
+
+
+ <p> Finally, many PROV
+ statements have other optional arguments or short forms that can be
+ used if none of the optional arguments is present. These are
+ handled by specific rules listed below. </p>
+
+<div class="definition" id="definition-short-forms"><div class="ruleTitle"><a class="internalDFN" href="#definition-short-forms">Definition 3 (definition-short-forms)</a></div>
+ <p>
+
+ </p><ol>
+ <li> <span class="name">activity(id,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">activity(id,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasGeneratedBy(id; e,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasGeneratedBy(id; e,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">used(id; a,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">used(id; a,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasStartedBy(id; a,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasStartedBy(id; a,-,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasEndedBy(id; a,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasEndedBy(id; a,-,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasInvalidatedBy(id; e,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasInvalidatedBy(id; e,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasDerivedFrom(id; e2,e1,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasDerivedFrom(id; e2,e1,-,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasAssociatedWith(id; e,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasAssociatedWith(id; e,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">actedOnBehalfOf(id; a2,a1,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">actedOnBehalfOf(id; a2,a1,-,attrs)</span>.
+ </li>
+ </ol>
+ </div>
+
+ <div class="remark">
+<!--<p>
+ Note that there is no expansion rule for <span class="name">wasDerivedFrom</span>. In a derivation of the form
+ <span class="name">wasDerivedFrom(id; e1,e2,attr)</span>, the
+ absence of the optional activity, generation and use identifiers
+ means that the derivation relationship may encompass multiple activities,
+generations, and uses. Thus, it is not equivalent to <span
+ class="name">wasDerivedFrom(id; e1,e2,a,g,u,attr)</span> where some
+ activity, generation and use are given explicitly.
+ The short
+ form is not defined in terms of the long form in this case.</p>-->
+
+ <p>
+There are no expansion rules for entity, agent, communication,
+ attribution, influence, alternate, or specialization
+ relations, because these
+ have no optional parameters aside from the identifier and attributes,
+ which are expanded by the rules in <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>
+ </div>
+
+<!--<div id="optional-attributes1"> -->
+<p id="optional-placeholders_text">Finally, most optional parameters (written <span class="name">-</span>) are, for the purpose of this document,
+ considered to be distinct, fresh existential variables. Optional parameters are defined in [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] and in [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>] for each type of PROV statement.
+ Thus,
+ before proceeding to apply other definitions or inferences, most
+ occurrences of <span class="name">-</span> are to be replaced
+ by fresh existential variables, distinct from any others occurring in
+ the instance.
+ The only exceptions to this general rule, where <span class="name">-</span> are to be left
+ in place, are the <a href="http://www.w3.org/TR/prov-dm/#derivation.activity">activity</a>, <a href="http://www.w3.org/TR/prov-dm/#derivation.generation">generation</a>, and <a href="http://www.w3.org/TR/prov-dm/#derivation.usage">usage</a> parameters in <span class="name">wasDerivedFrom</span> and
+ the <a href="http://www.w3.org/TR/prov-dm/#association.plan">plan</a>
+ parameter in <span class="name">wasAssociatedWith</span>. This is
+ further explained in remarks below.
+ </p>
+
+ <p>The treatment of optional parameters is specified formally using
+ the auxiliary concept of <dfn id="dfn-expandable-parameter">expandable parameter</dfn>. An
+ expandable parameter is one that can be omitted using the
+ placeholder <span class="name">-</span>, and if so, it is
+ to be replaced by a fresh existential identifier.
+ <a href="#expandable-parameters-fig">Table 3</a> defines the <a href="#dfn-expandable-parameter" class="internalDFN">expandable
+ parameter</a>s of the properties of PROV, needed in <a class="rule-ref" href="#optional-placeholders"><span>Definition 4 (optional-placeholders)</span></a>. For emphasis, the four optional parameters
+ that are not <a title="expandable parameter" href="#dfn-expandable-parameter" class="internalDFN">expandable</a> are
+ also listed. Parameters that cannot have value <span class="name">-</span>, and identifiers that are
+ expanded by <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a>, are not listed.</p>
+ <div id="expandable-parameters-fig">
+ <table id="expandable-parameters_table" border="1" class="thinborder" style="margin-left: auto; margin-right: auto; border-color: black;">
+<caption id="expandable-parameters">Table 3: Expandable and
+ Non-Expandable Parameters</caption>
+<tbody><tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+ <tr>
+ <th>Relation</th>
+ <th>Expandable </th>
+ <th>Non-expandable</th>
+ </tr>
+ <tr>
+ <td class="name">used(id; a,e,t,attrs)</td>
+ <td class="name">e,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasGeneratedBy(id; e,a,t,attrs)</td>
+ <td class="name">a,t</td>
+ <td></td>
+ </tr>
+<!-- <tr>
+ <td class="name">wasInformedBy(id; a2,a1,attrs)</td>
+ <td class="name"></td>
+ <td></td>
+ </tr>
+ -->
+ <tr>
+ <td class="name">wasStartedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">e,a1,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasEndedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">e,a1,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasInvalidatedBy(id; e,a,t,attrs)</td>
+ <td class="name">a,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasDerivedFrom(id; e2,e1,-,g,u,attrs)</td>
+ <td class="name"></td>
+ <td class="name">g,u</td>
+ </tr> <tr>
+ <td class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)<br>(where <span class="name">a</span> is not placeholder <span class="name">-</span>)</td>
+ <td class="name">g,u</td>
+ <td class="name">a</td>
+ </tr>
+
+<!--
+ <tr>
+ <td class="name">wasDerivedFrom(id; e2,e1,attrs)</td>
+ <td class="name"></td>
+ <td></td>
+ </tr>
+ -->
+<!-- <tr>
+ <td class="name">wasAttributedTo(id; e,ag,attr)</td>
+ <td class="name"></td>
+ <td></td>
+ </tr>
+ -->
+ <tr>
+ <td class="name">wasAssociatedWith(id; a,ag,pl,attrs)</td>
+ <td class="name">ag</td>
+ <td class="name">pl</td>
+ </tr>
+ <tr>
+ <td class="name">actedOnBehalfOf(id; ag2,ag1,a,attrs)</td>
+ <td class="name">a</td>
+ <td></td>
+ </tr>
+<!-- <tr>
+ <td class="name">wasInfluencedBy(id; o2,o1,attrs)</td>
+ <td class="name"></td>
+ <td></td>
+ </tr>
+ -->
+ </tbody></table>
+ </div>
+
+<p> <a class="rule-ref" href="#optional-placeholders"><span>Definition 4 (optional-placeholders)</span></a> states how parameters are to be expanded,
+ using the expandable parameters defined in <a href="#expandable-parameters-fig">Table 3</a>. The last two parts, 4 and 5,
+ indicate how to handle expansion of parameters for
+ <span class="name">wasDerivedFrom</span> expansion, which is only allowed for the
+ generation and use parameters when the activity is specified.
+ 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>
+
+
+<p> A later constraint, <a class="rule-ref" href="#impossible-unspecified-derivation-generation-use"><span>Constraint 51 (impossible-unspecified-derivation-generation-use)</span></a>,
+ forbids specifying generation and use parameters when the activity
+ is unspecified.</p>
+
+ <div class="definition" id="optional-placeholders"><div class="ruleTitle"><a class="internalDFN" href="#optional-placeholders">Definition 4 (optional-placeholders)</a></div>
+ <ol><li>
+ <span class="name">activity(id,-,t2,attrs)</span> <span class="conditional">IF AND ONLY
+ IF</span> there exists <span class="name">t1</span> such that <span class="name">activity(id,t1,t2,attrs)</span>. Here, <span class="name">t2</span> <em class="rfc2119" title="may">may</em> be a placeholder.
+ </li>
+<li> <span class="name">activity(id,t1,-,attrs)</span> <span class="conditional">IF AND ONLY
+ IF</span> there exists <span class="name">t2</span> such that <span class="name">activity(id,t1,t2,attrs)</span>. Here, <span class="name">t1</span> <em class="rfc2119" title="may">may</em> be a placeholder.
+</li>
+<!--
+<li>For each <span class="name">r</span> in {<span
+ class="name">entity</span>, <span class="name">activity</span>,
+ <span class="name">agent</span>}, the following definition
+ holds:
+ <p>
+ <span class="name">r(a<sub>0</sub>,...,a<sub>i-1</sub>, -, a<sub>i+1</sub>, ...,a<sub>n</sub>) </span> <span class="conditional">IF AND ONLY IF</span> there exists <span class="name">a'</span>
+ such that <span class="name">r(a<sub>0</sub>,...,a<sub>i-1</sub>,a',a<sub>i+1</sub>,...,a<sub>n</sub>)</span>.
+ </li>
+ -->
+ <li>For each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<!--<span class="name">wasInformedBy</span>,-->
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+<!--<span class="name">wasDerivedFrom</span>,-->
+<!--<span class="name">wasAttributedTo</span>,-->
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>
+ <!--<span class="name">wasInfluencedBy</span>
+ -->
+ }, if the <span class="name">i</span>th parameter
+ of <span class="name">r</span> is an <a href="#dfn-expandable-parameter" class="internalDFN">expandable parameter</a>
+ of <span class="name">r</span>
+ as specified in <a href="#expandable-parameters-fig">Table 3</a>
+then the following definition holds:
+ <p> <span class="name">r(a<sub>0</sub>;...,a<sub>i-1</sub>, -, a<sub>i+1</sub>, ...,a<sub>n</sub>) </span> <span class="conditional">IF AND ONLY IF</span> there exists <span class="name">a'</span>
+ such that <span class="name">r(a<sub>0</sub>;...,a<sub>i-1</sub>,a',a<sub>i+1</sub>,...,a<sub>n</sub>)</span>.
+ </p></li>
+ <li>If <span class="name">a</span> is not the placeholder <span class="name">-</span>, and <span class="name">u</span> is any term, then the following definition holds:
+ <p> <span class="name">wasDerivedFrom(id; e2,e1,a,-,u,attrs)</span> <span class="conditional">IF AND ONLY IF</span> there exists <span class="name">g</span>
+ such that <span class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)</span>.</p></li>
+ <li>If <span class="name">a</span> is not the placeholder <span class="name">-</span>, and <span class="name">g</span> is any term,
+ then the following definition holds:
+ <p> <span class="name">wasDerivedFrom(id; e2,e1,a,g,-,attrs)</span> <span class="conditional">IF AND ONLY IF</span> there exists <span class="name">u</span>
+ such that <span class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)</span>.</p></li></ol>
+ </div>
+
+ <div class="remark">
+<p>In an association of the form
+ <span class="name">wasAssociatedWith(id; a,ag,-,attr)</span>, the
+ absence of a plan means: either no plan exists, or a plan exists but
+ it is not identified. Thus, it is not equivalent to <span class="name">wasAssociatedWith(id; a,ag,p,attr)</span> where a
+ plan <span class="name">p</span> is given.</p>
+</div>
+ <div class="remark">
+<p> A derivation <span class="name">wasDerivedFrom(id; e2,e1,a,gen,use,attrs)</span> that
+ specifies an activity explicitly indicates that this activity achieved the derivation, with a usage <span class="name">use</span> of entity <span class="name">e1</span>, and a generation <span class="name">gen</span> of entity <span class="name">e2</span>.
+ It differs from a derivation of the form
+ <span class="name">wasDerivedFrom(id; e2,e1,-,-,-,attrs)</span> with
+ missing activity, generation, and usage. In the latter form, it is not specified
+ if one or more activities are involved in the derivation. </p>
+
+ <p>Let us consider a system, in which a derivation is underpinned by multiple activities. Conceptually, one could also model such a system with a new activity that encompasses the two original activities and underpins the derivation. The inferences defined in this specification do not allow the latter modelling to be inferred from the former. Hence, the two modellings of the same system are regarded as different in the context of this specification.</p>
+ </div>
+</section>
+
+<section id="entities-and-activities">
+ <h3><span class="secno">5.2 </span>Entities and Activities</h3>
+
+
+
+
+<p id="communication-generation-use-inference_text">Communication between activities <a title="definition" href="#definition" class="internalDFN">implies</a> the existence of an underlying
+entity generated by one activity and used by the other, and vice versa.</p>
+
+<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>
+<p>
+<span class="conditional">IF</span>
+<span class="name">wasInformedBy(_id; a2,a1,_attrs)</span>
+<span class="conditional">THEN</span>
+ there exist <span class="name">e</span>, <span class="name">_gen</span>, <span class="name">_t1</span>, <span class="name">_use</span>, and <span class="name">_t2</span>,
+such that <span class="name">wasGeneratedBy(_gen; e,a1,_t1,[])</span> and <span class="name">used(_use; a2,e,_t2,[])</span> hold.</p>
+</div>
+
+
+<p id="generation-use-communication-inference_text">
+
+ </p><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>
+<p>
+<span class="conditional">IF</span> <span class="name">wasGeneratedBy(_gen; e,a1,_t1,_attrs1)</span>
+ and <span class="name">used(_id2; a2,e,_t2,_attrs2)</span> hold
+ <span class="conditional">THEN</span>
+ there exists <span class="name">_id</span>
+such that <span class="name">wasInformedBy(_id; a2,a1,[])</span>
+</p></div>
+
+
+ <div class="remark">
+<p>The relationship <span class="name">wasInformedBy</span> is not
+<a href="#dfn-transitive" class="internalDFN">transitive</a>. Indeed, consider the following statements.</p>
+<pre class="codeexample">wasInformedBy(a2,a1)
+wasInformedBy(a3,a2)
+</pre>
+<p> We cannot infer <span class="name">wasInformedBy(a3,a1)</span>
+ from these statements alone. Indeed,
+from
+<span class="name">wasInformedBy(a2,a1)</span>, we know that there exists <span class="name">e1</span> such that <span class="name">e1</span> was generated by <span class="name">a1</span>
+and used by <span class="name">a2</span>. Likewise, from <span class="name">wasInformedBy(a3,a2)</span>, we know that there exists <span class="name">e2</span> such that <span class="name">e2</span> was generated by <span class="name">a2</span>
+and used by <span class="name">a3</span>. The following illustration
+shows a counterexample to transitivity. The
+horizontal axis represents the event line. We see that <span class="name">e1</span> was generated after <span class="name">e2</span> was used. Furthermore, the illustration also shows that
+<span class="name">a3</span> completes before <span class="name">a1</span> started. So in this example (with no other
+ information) it is impossible for <span class="name">a3</span> to have used an entity generated by <span class="name">a1</span>. This is illustrated in <a href="#counterexample-wasInformedBy">Figure 2</a>.</p>
+
+<div style="text-align: center;">
+<span class="figure" id="fig-figure-2-counter-example-for-transitivity-of-wasinformedby">
+<img src="images/constraints/informedByNonTransitive.png" alt="non transitivity of wasInformedBy">
+<br>
+<span class="figcaption" id="counterexample-wasInformedBy">Figure 2<sup><a class="internalDFN" href="#counterexample-wasInformedBy"><span class="diamond"> ◊:</span></a></sup> Counter-example for transitivity of wasInformedBy</span>
+</span> <!-- <b>Figure 2:</b> -->
+</div>
+</div>
+
+<!--
+<div class="note">
+ The following two inferences could interact with type inference to produce
+ nontermination. For example, once we have an activity we can use
+ activity-start-end-inference and start-type-inference forever to
+ infer an infinite chain of activities, each starting the next.
+ Similarly, we can use inference-activity-start-end,
+start-type-inference, entity-generation-invalidation-inference,
+ and generation-type-inference forever to infer an infinite chain of
+ entities generated by activities that were started by entities that
+ were generated by activities ...
+
+ We must break this recursion somewhere in order to ensure
+ implementability. I propose to drop both of the following
+ inferences, since they seem less necessary than the type inferences.
+ </div>
+-->
+
+<hr>
+
+<!--
+ <div class="note">
+ The following inference is a "<a
+href="http://www.w3.org/2005/10/Process-20051014/tr#cfi">feature at
+risk</a>" and may be dropped if it leads to
+ implementation difficulties.
+ </div>
+-->
+
+<p id="entity-generation-invalidation-inference_text">
+From an entity statement, we can infer the existence of
+generation and invalidation events.
+</p>
+<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>
+<p>
+<span class="conditional">IF</span> <span class="name">entity(e,_attrs)</span> <span class="conditional">THEN</span> there exist
+<span class="name">_gen</span>, <span class="name">_a1</span>, <span class="name">_t1</span>,
+<span class="name">_inv</span>, <span class="name">_a2</span>, and <span class="name">_t2</span> such that
+ <span class="name">wasGeneratedBy(_gen; e,_a1,_t1,[])</span> and <span class="name">wasInvalidatedBy(_inv; e,_a2,_t2,[])</span>.
+</p></div>
+
+
+<hr>
+<!--
+ <div class="note">
+ The following inference is a "<a
+href="http://www.w3.org/2005/10/Process-20051014/tr#cfi">feature at
+risk</a>" and may be dropped if it leads to
+ implementation difficulties.
+ </div>-->
+
+<p id="activity-start-end-inference_text">
+From an activity statement, we can infer
+start and end events whose times match the start and end times of
+the activity, respectively.
+</p>
+<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>
+<p>
+<span class="conditional">IF</span> <span class="name">activity(a,t1,t2,_attrs)</span> <span class="conditional">THEN</span> there exist <span class="name">_start</span>, <span class="name">_e1</span>, <span class="name">_a1</span>, <span class="name">_end</span>, <span class="name">_a2</span>,
+ and <span class="name">_e2</span> such that
+ <span class="name">wasStartedBy(_start; a,_e1,_a1,t1,[])</span> and <span class="name">wasEndedBy(_end; a,_e2,_a2,t2,[])</span>.
+</p></div>
+
+
+<hr>
+
+
+<p id="wasStartedBy-inference_text">The start of an activity <span class="name">a</span> triggered by entity <span class="name">e1</span>
+implies that
+<span class="name">e1</span> was generated by the starting activity <span class="name">a1</span>.</p>
+
+<div class="inference" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div>
+<p><span class="conditional">IF</span>
+ <span class="name">wasStartedBy(_id; a,e1,a1,_t,_attrs)</span>,
+<span class="conditional">THEN</span> there exist <span class="name">_gen</span> and <span class="name">_t1</span>
+such that
+ <span class="name">wasGeneratedBy(_gen; e1,a1,_t1,[])</span>.</p>
+</div>
+<p>
+
+</p><hr>
+
+<p id="wasEndedBy-inference_text">Likewise,
+the ending of activity <span class="name">a</span> by triggering entity <span class="name">e1</span> implies that
+<span class="name">e1</span> was generated by the ending activity <span class="name">a1</span>.
+</p>
+
+<div class="inference" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div>
+<p><span class="conditional">IF</span>
+ <span class="name">wasEndedBy(_id; a,e1,a1,_t,_attrs)</span>,
+<span class="conditional">THEN</span> there exist <span class="name">_gen</span> and <span class="name">_t1</span> such that
+ <span class="name">wasGeneratedBy(_gen; e1,a1,_t1,[])</span>.</p>
+</div>
+
+
+
+
+</section>
+
+ <section id="derivations">
+<h3><span class="secno">5.3 </span>Derivations</h3>
+
+
+<hr>
+<p id="derivation-generation-use-inference_text">Derivations with explicit
+activity, generation, and usage admit the following inference: </p>
+
+<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>
+<p> In this inference, none of <span class="name">a</span>, <span class="name">gen2</span> or <span class="name">use1</span> can be
+ placeholders <span class="name">-</span>.
+ </p><p>
+<span class="conditional">IF</span> <span class="name">wasDerivedFrom(_id; e2,e1,a,gen2,use1,_attrs)</span>,
+ <span class="conditional">THEN</span> there exists <span class="name">_t1</span> and <span class="name">_t2</span> such that <span class="name">used(use1; a,e1,_t1,[])</span> and <span class="name">wasGeneratedBy(gen2; e2,a,_t2,[])</span>.
+</p>
+</div>
+<p>
+<!--
+<hr>
+
+<p id='derivation-use-inference_text'>According to <a class="rule-text"
+href="#optional-placeholders"><span>TBD</span></a>, optional generation and usage in a derivation are not expandable. However, derivations with an explicit activity and
+no specified generation and usage admit the following inference: </p>
+
+
+<div class="note">
+ derivation-use-inference is problematic because the inferred
+ derivation may violate the key constraint on derivations. We could
+conditionally allow expansion of gen and use when the activity is
+ specified (non-placeholder).
+</div>
+<div class='inference' id='derivation-use-inference'>
+<p>
+ In this inference, <span class="name">a</span> cannot be
+ a placeholder <span class="name">-</span>.
+ </p>
+ <p>
+<span class='conditional'>IF</span> <span class="name">wasDerivedFrom(id; e2,e1,a,-,-,attrs)</span> and <span class="name">wasGeneratedBy(gen; e2,a,_t2,_attrs2)</span> hold, <span
+class='conditional'>THEN</span> there exist <span
+ class="name">_t1</span> and <span class="name">use</span> such
+ that <span class="name">used(use; a,e1,_t1,[])</span> and <span
+ class="name">wasDerivedFrom(id; e2,e1,a,gen,use,attrs)</span>.
+</div>
+<p>This inference is justified by the fact that the entity denoted by
+ <span class="name">e2</span> has a unique generation event
+ representing its generation by activity <span class="name">a</span>
+(see <a class="rule-text" href="#unique-generation"><span>TBD</span></a>). Hence, this activity is also the one referred to by the usage of <span class="name">e1</span>.
+</p>
+
+<div class="remark" id="derivation-generation-use-inference-remark">
+ <p>
+ <a class="rule-text" href="#derivation-use-inference"><span>TBD</span></a> allows "-" to be replaced by existential variables in a <span
+ class="name">wasDerivedFrom</span>, when an activity is explicit, and a generation known.</p>
+
+<p> However, a derivation without explicit generation and usage cannot be normalized even when a generation and usage hold.
+if <span class="name">wasDerivedFrom(id; e2,e1,a,-,-,attrs)</span>,
+<span class="name">wasGeneratedBy(gen; e2,a,_t2,_attrs2)</span>,
+and <span class="name">used(use; a,e1,_t1,[])</span>, it is not
+ necessarily the case that
+<span
+ class="name">wasDerivedFrom(id; e2,e1,a,gen,use,attrs)</span>.
+Indeed,
+<span
+class="name">e1</span> may be used multiple times by
+ <span class="name">a</span>, usage <span class="name">use</span>
+may not be involved in the derivation (for example, it may well have taken place after
+the generation of <span
+expanclass="name">e2</span>).</p>
+ </div>
+-->
+
+<!--
+ <hr />
+ <div class="note">
+ Likely to delete specific-derivation-inference
+ </div>
+<p id="specific-derivation-inference_text">A derivation
+ specifying activity, generation and use events is a special case of
+ a derivation that leaves these unspecified. The converse is not
+ the case because the activity parameter of derivations is
+ non-expandable in <a class="rule-ref"
+href="#optional-placeholders"><span>TBD</span></a>. </p>
+
+<div class='inference' id='specific-derivation-inference'>
+<p>In this inference, <span class="name">_act</span>, <span class="name">_gen</span>, and <span class="name">_use</span> MUST NOT
+ be placeholders.
+ </p>
+ <p><span class='conditional'>IF</span> <span
+ class="name">wasDerivedFrom(id; e2,e1,_act,_gen,_use,attrs)</span>,
+<span class='conditional'>THEN</span> <span
+ class="name">wasDerivedFrom(id; e2,e1,-,-,-,attrs)</span>.
+</p>
+</div>
+-->
+
+</p><hr>
+<p id="revision-is-alternate-inference_text">A revision admits the following inference, stating that the two entities
+linked by a revision are also alternates.</p>
+
+<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>
+ <p>In this inference, any of <span class="name">_a</span>, <span class="name">_g</span> or <span class="name">_u</span> <em class="rfc2119" title="may">may</em> be placeholders.</p>
+<p>
+ <span class="conditional">IF</span> <span class="name">wasDerivedFrom(_id; e2,e1,_a,_g,_u,[prov:type='prov:Revision'])</span>, <span class="conditional">THEN</span> <span class="name">alternateOf(e2,e1)</span>.
+</p>
+<!--
+<li><span class='conditional'>IF</span> <span
+ class="name">wasDerivedFrom(_id; e2,e1,_act,_gen,_use,[prov:type='prov:Revision'])</span>, <span class='conditional'>THEN</span> <span
+ class="name">alternateOf(e2,e1)</span>.
+</li>
+-->
+</div>
+
+
+<!--
+<div class="note">
+ The following doesn't make sense because wasRevisionOf and
+ wasDerivedFrom have different types.
+ </div>
+<p><span class="name">wasRevisionOf</span> is a strict sub-relation
+ of <span class="name">wasDerivedFrom</span> since two entities <span class="name">e2</span> and <span class="name">e1</span>
+ may satisfy <span class="name">wasDerivedFrom(e2,e1)</span> without being a variant of
+ each other.
+</p>
+
+
+ <div class="note">
+ Motivation for quotation inference
+ </div>
+<div class='inference' id='quotation-implication'>
+<span class='conditional'>IF</span>
+<span class="name">wasQuotedFrom(e2,e1,ag2,ag1,attrs)</span>
+ for some identifiers
+<span class="name">e2</span>, <span class="name">e1</span>, <span class="name">ag2</span>, <span class="name">ag1</span>,
+<span class='conditional'>THEN</span>
+<pre
+wasDerivedFrom(e2,e1)
+wasAttributedTo(e2,ag2)
+wasAttributedTo(e1,ag1)
+</pre>
+</div>
+
+<p>
+
+-->
+
+<div class="remark">
+ There is no inference stating that <span class="name">wasDerivedFrom</span> is
+ transitive.
+ </div>
+</section>
+
+
+<section id="agents">
+<h3><span class="secno">5.4 </span>Agents</h3>
+
+<p id="attribution-inference_text"> Attribution is the ascribing of an entity to an agent. An
+entity can only be ascribed to an agent if the agent was associated with
+an activity that generated the entity. If the activity, generation
+and association events are not explicit in the instance, they can
+be inferred.</p>
+
+<div class="inference" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">wasAttributedTo(_att; e,ag,_attrs)</span>
+ <!--holds for some identifiers
+<span class="name">e</span> and <span class="name">ag</span>, -->
+<span class="conditional">THEN</span> there exist
+ <span class="name">a</span>,
+ <span class="name">_t</span>,
+<span class="name">_gen</span>,
+<span class="name">_assoc</span>,
+ <span class="name">_pl</span>,
+such that
+<span class="name">wasGeneratedBy(_gen; e,a,_t,[])</span> and
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,[])</span>.
+</p>
+</div>
+
+<div class="remark">
+ In the above inference, <span class="name">_pl</span> is an
+ existential variable, so it can be unified
+with a constant identifier, another existential variable, or a
+ placeholder <span class="name">-</span>, as explained
+ in the definition of <a>unification</a>.
+ </div>
+<hr>
+<p id="delegation-inference_text"> Delegation relates agents where one agent acts on behalf of
+another, in the context of some activity. The supervising agent
+delegates some responsibility for part of the activity to the
+subordinate agent, while retaining some responsibility for the overall
+activity. Both agents are associated with this activity.</p>
+
+
+<div class="inference" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">actedOnBehalfOf(_id; ag1, ag2, a, _attrs)</span>
+<span class="conditional">THEN</span> there exist <span class="name">_id1</span>, <span class="name">_pl1</span>, <span class="name">_id2</span>, and <span class="name">_pl2</span> such that <span class="name">wasAssociatedWith(_id1; a, ag1, _pl1, [])</span>
+ and <span class="name">wasAssociatedWith(_id2; a, ag2, _pl2,
+ [])</span>.
+</p>
+</div>
+
+
+<div class="remark">
+ The two associations between the agents and the activity
+ may have different identifiers, different plans, and different
+ attributes. In particular, the plans of the two agents need not be
+ the same, and one, both, or neither can be the placeholder <span class="name">-</span>
+ indicating that there is no plan, because the existential variables
+ <span class="name">_pl1</span> and <span class="name">_pl2</span>
+ can be replaced with constant identifiers, existential variables, or
+ placeholders <span class="name">-</span> independently, as explained
+ in the definition of <a>unification</a>.
+ </div>
+
+<hr>
+<p id="influence-inference_text">
+The <span class="name">wasInfluencedBy</span> relation is implied by other relations, including
+usage, start, end, generation, invalidation, communication,
+derivation, attribution, association, and delegation. To capture this
+explicitly, we allow the following inferences:
+</p>
+<div class="inference" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div>
+<p>
+ </p><ol>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasGeneratedBy(id; e,a,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e, a, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">used(id; a,e,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a, e, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasInformedBy(id; a2,a1,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a2, a1, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasStartedBy(id; a2,e,a1,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a2, e, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasEndedBy(id; a2,e,_a1,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a2, e, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasInvalidatedBy(id; e,a,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e, a, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasDerivedFrom(id; e2, e1, a, g, u, attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e2, e1, attrs)</span>. Here,
+ <span class="name">a</span>, <span class="name">g</span>, <span class="name">u</span> <em class="rfc2119" title="may">may</em> be placeholders <span class="name">-</span>.
+ </li>
+<li>
+ <span class="conditional">IF</span> <span class="name">wasAttributedTo(id; e,ag,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e, ag, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasAssociatedWith(id; a,ag,_pl,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a, ag, attrs)</span>. Here,
+ <span class="name">_pl</span> <em class="rfc2119" title="may">may</em> be a placeholder <span class="name">-</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">actedOnBehalfOf(id; ag2,ag1,_a,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; ag2, ag1, attrs)</span>.
+ </li>
+</ol>
+</div>
+
+<div class="remark">
+ The inferences above permit the use of same identifier for an
+ influence relationship and a more
+ specific relationship.
+</div>
+
+</section>
+
+
+
+ <section id="alternate-and-specialized-entities">
+<h3><span class="secno">5.5 </span>Alternate and Specialized Entities</h3>
+
+
+
+
+<hr>
+ <p id="alternate-reflexive_text">The relation <span class="name">alternateOf</span> is an <a href="#dfn-equivalence-relation" class="internalDFN">equivalence relation</a> on
+ entities: that is,
+ it is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>,
+ <a href="#dfn-transitive" class="internalDFN">transitive</a> and <a href="#dfn-symmetric" class="internalDFN">symmetric</a>. As a consequence, the
+ following inferences can be applied:</p>
+
+
+<div class="inference" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">entity(e)</span> <span class="conditional">THEN</span>
+<span class="name">alternateOf(e,e)</span>.
+</p>
+ </div>
+
+<p>
+
+</p><hr>
+ <p id="alternate-transitive_text">
+
+ </p><div class="inference" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div>
+<p><!-- For any entities <span class='name'>e1</span>, <span class='name'>e2</span>, <span class='name'>e3</span>, -->
+<span class="conditional">IF</span> <span class="name">alternateOf(e1,e2)</span> and
+ <span class="name">alternateOf(e2,e3)</span> <span class="conditional">THEN</span> <span class="name">alternateOf(e1,e3)</span>.</p>
+ </div>
+
+<p>
+
+</p><hr>
+ <p id="alternate-symmetric_text">
+
+ </p><div class="inference" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div>
+<p><!-- For any entity <span class='name'>e1</span>, <span class='name'>e2</span>, -->
+<span class="conditional">IF</span> <span class="name">alternateOf(e1,e2)</span> <span class="conditional">THEN</span> <span class="name">alternateOf(e2,e1)</span>.</p>
+ </div>
+
+<p>
+
+
+</p><hr>
+<p id="specialization-transitive_text">
+Similarly, specialization is a
+ <a href="#dfn-strict-partial-order" class="internalDFN">strict partial order</a>: it is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>. Irreflexivity is handled later as <a class="rule-ref" href="#impossible-specialization-reflexive"><span>Constraint 52 (impossible-specialization-reflexive)</span></a>
+ </p>
+ <div class="inference" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div>
+<p>
+<!-- For any entities <span class='name'>e1</span>, <span class='name'>e2</span>, <span class='name'>e3</span>, -->
+<span class="conditional">IF</span> <span class="name">specializationOf(e1,e2)</span>
+ and
+ <span class="name">specializationOf(e2,e3)</span> <span class="conditional">THEN</span> <span class="name">specializationOf(e1,e3)</span>.</p>
+ </div>
+
+<p>
+
+</p><hr>
+
+ <p id="specialization-alternate-inference_text">If one entity specializes another, then they are also
+ alternates:</p>
+
+ <div class="inference" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div>
+<p>
+<!-- For any entities <span class='name'>e1</span>, <span class='name'>e2</span>, -->
+<span class="conditional">IF</span> <span class="name">specializationOf(e1,e2)</span> <span class="conditional">THEN</span> <span class="name">alternateOf(e1,e2)</span>.</p>
+ </div>
+
+<hr>
+<p id="specialization-attributes-inference_text">
+ If one entity specializes another then all attributes of the more
+ general entity are also attributes of the more specific one.
+ </p>
+<div class="inference" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div>
+ <p>
+<!-- For any entities <span class='name'>e1</span>, <span class='name'>e2</span>,-->
+<span class="conditional">IF</span> <span class="name">entity(e1, attrs)</span> <!--holds for some
+ attributes <span class='name'>attrs</span>
+ --> and <span class="name">specializationOf(e2,e1)</span>, <span class="conditional">THEN </span>
+ <span class="name">entity(e2, attrs)</span>.</p>
+ </div>
+
+
+
+<!--
+ <hr />
+
+ <div class="note">
+<p>Note: The following inference is associated with a feature "<a href="http://www.w3.org/2005/10/Process-20051014/tr#cfi">at risk</a>" and may be removed from this specification based on feedback. Please send feedback to public-prov-comments@w3.org.</p>
+</div>
+
+
+ <p id="mention-specialization-inference_text">If one entity is a mention of another in a bundle, then the former is also a specialization of the latter:</p>
+
+ <div class='inference' id="mention-specialization-inference">
+<p>
+<span class='conditional'>IF</span> <span class='name'>mentionOf(e2,e1,b)</span> <span class='conditional'>THEN</span> <span class='name'>specializationOf(e2,e1)</span>.</p>
+ </div>
+
+-->
+</section>
+
+
+
+
+
+</section>
+
+
+
+<section id="constraints">
+<!--OddPage--><h2><span class="secno">6. </span>Constraints</h2>
+
+
+
+
+<p>
+This section defines a collection of constraints on PROV instances.
+There are three kinds of constraints:
+ </p><ul><li><em>uniqueness constraints</em> that say that a <a href="#instance" class="internalDFN">PROV
+ instance</a> can contain at most one statement of each kind with a
+ given identifier. For
+ example, if we describe the same generation event twice, then the
+ two statements should have the same times;
+ </li>
+ <li> <em>event ordering constraints</em> that say that it
+ should be possible to arrange the
+ events (generation, usage, invalidation, start, end) described in a
+ PROV instance into a <a href="#dfn-preorder" class="internalDFN">preorder</a> that corresponds to a sensible
+ "history" (for example, an entity should not be generated after it
+ is used); and
+ </li>
+ <li><em>impossibility constraints</em>, which forbid certain
+ patterns of statements in <a href="#dfn-valid" class="internalDFN">valid</a> PROV instances.
+ </li></ul>
+
+ <p>As in a definition or inference, term symbols such as <span class="name">id</span>,
+ <span class="name">start</span>, <span class="name">end</span>, <span class="name">e</span>,
+ <span class="name">a</span>, <span class="name">attrs</span> in a constraint,
+ are assumed to be variables unless otherwise specified. These variables are scoped at
+ the constraint level, so the rule is equivalent to any one-for-one
+ renaming of the variable names. When several rules are collected within a constraint
+ as an ordered list, the scope of the variables in each rule is at the level of list elements, and so reuse of
+ variable names in different rules does not affect the meaning.
+</p>
+ <section id="uniqueness-constraints">
+
+
+
+ <h3><span class="secno">6.1 </span>Uniqueness Constraints</h3>
+
+
+
+ <p> In the absence of existential variables, uniqueness constraints
+ could be checked directly by checking that no identifier appears
+ more than once for a given statement. However, in the presence of
+ existential variables, we need to be more careful to combine
+ partial information that might be present in multiple compatible
+ statements, due to inferences. Uniqueness constraints are
+ enforced through <a href="#dfn-merging" class="internalDFN">merging</a> pairs of statements subject to
+ equalities. For example, suppose we have two activity statements
+ <span class="name">activity(a,2011-11-16T16:00:00,_t1,[a=1])</span> and <span class="name">activity(a,_t2,2011-11-16T18:00:00,[b=2])</span>, with existential variables <span class="name">_t1</span> and <span class="name">_t2</span>. The <a>merge</a> of
+ these two statements (describing the same activity <span class="name">a</span>) is <span class="name">activity(a,2011-11-16T16:00:00,2011-11-16T18:00:00,[a=1,b=2])</span>. </p>
+
+
+ <p>
+A typical uniqueness constraint is as follows:
+ </p>
+ <div class="constraint-example" id="uniqueness-example"><div class="ruleTitle"><a class="internalDFN" href="#uniqueness-example">Constraint-example NNN (uniqueness-example)</a></div>
+<p> <span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span> <span class="conditional">THEN</span> <span class="name">t<sub>1</sub></span> = <span class="name">u<sub>1</sub></span> and ... and <span class="name">t<sub>n</sub></span> = <span class="name">u<sub>n</sub></span>.</p>
+ </div>
+
+ <p> Such a constraint is enforced as follows:</p>
+ <ol> <li>Suppose PROV instance <span class="math">I</span> contains all of the hypotheses
+ <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span>.
+ </li>
+ <li>Attempt to unify all of the equated terms in the conclusion
+ <span class="name">t<sub>1</sub></span> = <span class="name">u<sub>1</sub></span> and ... and <span class="name">t<sub>n</sub></span> = <span class="name">u<sub>n</sub></span>.
+ </li>
+ <li>If unification fails, then the constraint
+ is unsatisfiable, so application of the constraint to <span class="math">I</span>
+ fails. If this failure occurs during <a>normalization</a> prior to
+validation, then <span class="math">I</span> is invalid, as explained in <a href="#normalization-validity-equivalence">Section 6</a>.
+ </li>
+ <li>If unification succeeds with a substitution <span class="math">S</span>, then
+ <span class="math">S</span> is applied to the instance <span class="math">I</span>, yielding result <span class="math">S(I)</span>.</li>
+ </ol>
+
+<p> <em><dfn id="dfn-key-constraints">Key constraints</dfn></em> are uniqueness constraints
+ that specify that a particular key field of a relation uniquely
+ determines the other parameters. Key constraints are written as follows:
+ </p>
+
+ <div class="constraint-example" id="key-example"><div class="ruleTitle"><a class="internalDFN" href="#key-example">Constraint-example NNN (key-example)</a></div>
+ <p>The <span class="name">a<sub>k</sub></span> field is a <span class="conditional">KEY</span> for relation <span class="name">r(a<sub>0</sub>; a<sub>1</sub>,...,a<sub>n</sub>)</span>. </p></div>
+
+ <p> Because of the presence of attributes, key constraints do not
+ reduce directly to uniqueness constraints. Instead, we enforce key
+ constraints using the following <dfn id="dfn-merging">merging</dfn> process. </p>
+ <ol>
+ <li> Suppose <span class="name">r(a<sub>0</sub>; a<sub>1</sub>,...a<sub>n</sub>,attrs1)</span> and <span class="name">r(b<sub>0</sub>; b<sub>1</sub>,...b<sub>n</sub>,attrs2)</span> hold in PROV instance <span class="math">I</span>, where the key fields <span class="name">a<sub>k</sub> = b<sub>k</sub></span> are equal.</li>
+ <li> Attempt to unify all of the corresponding parameters <span class="name">a<sub>0</sub> = b<sub>0</sub> </span> and ... and <span class="name">a<sub>n</sub> = b<sub>n</sub></span>.
+ </li>
+ <li>If unification fails, then the constraint is unsatisfiable, so
+ application of the key constraint to <span class="math">I</span> fails.
+ </li>
+ <li>If unification succeeds with substitution <span class="math">S</span>, then we remove <span class="name">r(a<sub>0</sub>; a<sub>1</sub>,...a<sub>n</sub>,attrs1)</span> and <span class="name">r(b<sub>0</sub>; b<sub>1</sub>,...b<sub>n</sub>,attrs2)</span> from <span class="math">I</span>, obtaining
+ instance <span class="math">I'</span>, and return instance <span class="name">{r(S(a<sub>0</sub>); S(a<sub>1</sub>),...S(a<sub>n</sub>),attrs1 ∪
+ attrs2)}</span> ∪ <span class="math">S(I')</span>.
+ </li></ol>
+
+
+
+<p>Thus, if a PROV instance contains an apparent violation of a uniqueness
+ constraint or key constraint, unification or merging can be used to determine
+ whether the constraint can be satisfied by instantiating some existential
+ variables with other terms. For key constraints, this is the same
+ as merging pairs of statements whose keys are equal and whose
+ corresponding arguments are compatible, because after
+ unifying respective arguments and combining attribute lists, the two statements
+ become equal and one can be omitted. </p>
+
+
+
+
+
+
+<p>
+</p><hr>
+
+ <p id="key-object_text">The various identified objects of PROV <em class="rfc2119" title="must">must</em> have
+ unique statements describing them within a valid PROV instance.
+ This is enforced through
+ the following key constraints:
+ </p>
+ <div class="constraint" id="key-object"><div class="ruleTitle"><a class="internalDFN" href="#key-object">Constraint 22 (key-object)</a></div>
+<p></p><ol>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#entity.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">entity(id,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#activity.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">activity(id,t1,t2,attrs)</span> statement.
+ </li>
+<li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#agent.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">agent(id,attrs)</span> statement.
+ </li>
+ </ol>
+ </div>
+
+ <hr>
+ <p id="key-properties_text"> Likewise, the statements
+in a valid PROV instance must provide consistent information about
+ each identified object or relationship. The following key
+ constraints require that all of the information about each identified
+ statement can be merged into a single, consistent statement:
+ </p>
+ <div class="constraint" id="key-properties"><div class="ruleTitle"><a class="internalDFN" href="#key-properties">Constraint 23 (key-properties)</a></div>
+<p></p><ol>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#generation.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasGeneratedBy(id; e,a,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#usage.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">used(id; a,e,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#communication.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasInformedBy(id; a2,a1,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#start.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasStartedBy(id; a2,e,a1,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#end.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasEndedBy(id; a2,e,a1,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#invalidation.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasInvalidatedBy(id; e,a,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#derivation.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasDerivedFrom(id; e2, e1, a, g2, u1, attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#attribution.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasAttributedTo(id; e,ag,attr)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#association.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasAssociatedWith(id; a,ag,pl,attrs)</span> statement.
+ </li>
+<!--
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#association.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasAssociatedWith(id; a,ag,-,attrs)</span> statement.
+ </li>
+-->
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#delegation.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">actedOnBehalfOf(id; ag2,ag1,a,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#influence.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasInfluencedBy(id; o2,o1,attrs)</span> statement.
+ </li>
+</ol>
+ </div>
+
+
+
+<hr>
+
+
+<div id="unique-generation_text">
+<p> Entities may have multiple generation or invalidation events
+ (either or both may, however, be left implicit). An entity can be
+ generated by more than one activity, with one generation event per
+ each entity-activity pair. These events must be simultaneous, as required by <a class="rule-ref" href="#generation-generation-ordering"><span>Constraint 39 (generation-generation-ordering)</span></a>
+ and <a class="rule-ref" href="#invalidation-invalidation-ordering"><span>Constraint 40 (invalidation-invalidation-ordering)</span></a>.
+<!-- Together with the key constraints above, this implies that
+ <span class="name">e</span> is also a key for generation and
+ invalidation statements.
+ -->
+</p>
+</div>
+
+
+<div class="constraint" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint 24 (unique-generation)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasGeneratedBy(gen1; e,a,_t1,_attrs1)</span> and <span class="name">wasGeneratedBy(gen2; e,a,_t2,_attrs2)</span>,
+<span class="conditional">THEN</span> <span class="name">gen1</span> = <span class="name">gen2</span>.</p>
+</div>
+
+<p>
+
+</p><hr>
+<p id="unique-invalidation_text">
+
+</p><div class="constraint" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint 25 (unique-invalidation)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasInvalidatedBy(inv1; e,a,_t1,_attrs1)</span> and <span class="name">wasInvalidatedBy(inv2; e,a,_t2,_attrs2)</span>,
+<span class="conditional">THEN</span> <span class="name">inv1</span> = <span class="name">inv2</span>.</p>
+</div>
+
+
+<div class="remark"> <p> It follows from the above uniqueness and key
+ constraints that the generation and invalidation events linking an
+ entity and activity are unique, if specified. However, because we
+ apply the constraints by merging, it is possible for a valid PROV instance
+to contain multiple statements about the same generation or
+ invalidation event, for example:</p>
+ <pre>wasGeneratedBy(id1; e,a,-,[prov:location="Paris"])
+wasGeneratedBy(-; e,a,-,[color="Red"])
+</pre>
+<p> When the uniqueness and key constraints are applied, the instance is
+ <a title="normal form" href="#dfn-normal-form" class="internalDFN">normalized</a> to the following form:</p>
+ <pre>wasGeneratedBy(id1; e,a,_t,[prov:location="Paris",color="Red"])
+</pre>
+<p>
+ where <span class="name">_t</span> is a new existential variable.
+ </p>
+</div>
+
+
+<hr>
+<p id="unique-wasStartedBy_text">
+An activity may have more than one start and
+end event, each having a different activity (either or both may,
+however, be left implicit). However,
+the triggering entity linking any two activities in a start or end event is unique.
+That is, an activity may be started by
+several other activities, with shared or separate triggering
+entities. If an activity is started or ended by multiple events, they must all
+be simultaneous, as specified in <a class="rule-ref" href="#start-start-ordering"><span>Constraint 31 (start-start-ordering)</span></a>
+and <a class="rule-ref" href="#end-end-ordering"><span>Constraint 32 (end-end-ordering)</span></a>.
+</p>
+
+<div class="constraint" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint 26 (unique-wasStartedBy)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasStartedBy(start1; a,_e1,a0,_t1,_attrs1)</span> and <span class="name">wasStartedBy(start2; a,_e2,a0,_t2,_attrs2)</span>, <span class="conditional">THEN</span> <span class="name">start1</span> = <span class="name">start2</span>.</p>
+</div>
+
+<p id="unique-wasEndedBy_text">
+
+</p><div class="constraint" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint 27 (unique-wasEndedBy)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasEndedBy(end1; a,_e1,a0,_t1,_attrs1)</span> and <span class="name">wasEndedBy(end2; a,_e2,a0,_t2,_attrs2)</span>, <span class="conditional">THEN</span> <span class="name">end1</span> = <span class="name">end2</span>.</p>
+</div>
+
+
+<hr>
+
+
+
+
+
+ <p id="unique-startTime_text">An <a href="#dfn-start-event" class="internalDFN">activity start event</a> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity starts. It allows for an optional time attribute. <span id="optional-start-time">Activities also allow for an optional start time attribute. If both are specified, they <em class="rfc2119" title="must">must</em> be the same, as expressed by the following constraint.</span>
+</p>
+
+<div class="constraint" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint 28 (unique-startTime)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">activity(a2,t1,_t2,_attrs)</span> and <span class="name">wasStartedBy(_start; a2,_e,_a1,t,_attrs)</span>, <span class="conditional">THEN</span> <span class="name">t1</span>=<span class="name">t</span>.</p>
+</div>
+
+<hr>
+
+<p id="unique-endTime_text">An <a href="#dfn-end-event" class="internalDFN">activity end event</a> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity ends. It allows for an optional time attribute. <span id="optional-end-time">Activities also allow for an optional end time attribute. If both are specified, they <em class="rfc2119" title="must">must</em> be the same, as expressed by the following constraint.</span>
+</p>
+
+<div class="constraint" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint 29 (unique-endTime)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">activity(a2,_t1,t2,_attrs)</span> and <span class="name">wasEndedBy(_end; a2,_e,_a1,t,_attrs1)</span>, <span class="conditional">THEN</span> <span class="name">t2</span> = <span class="name">t</span>.</p>
+</div>
+
+<p>
+
+
+</p><hr>
+
+
+<!--
+<div class="note">
+<p>Note: The following constraint is associated with a feature "<a href="http://www.w3.org/2005/10/Process-20051014/tr#cfi">at risk</a>" and may be removed from this specification based on feedback. Please send feedback to public-prov-comments@w3.org.</p>
+</div>
+
+
+<div id='unique-mention_text'>
+<p>An entity can be the subject of at most one mention relation.</p>
+</div>
+
+
+<div class='constraint' id='unique-mention'>
+<p>
+<span class='conditional'>IF</span> <span class="name">mentionOf(e, e1, b1)</span> and <span class="name">mentionOf(e, e2, b2)</span>,
+<span class='conditional'>THEN</span> <span class="name">e1</span>=<span class="name">e2</span> and <span class="name">b1</span>=<span class="name">b2</span>.</p>
+</div>
+
+-->
+
+
+
+</section> <!-- uniqueness-constraints-->
+
+<section id="event-ordering-constraints">
+<h3><span class="secno">6.2 </span>Event Ordering Constraints</h3>
+
+
+<p>Given that provenance consists of a description of past entities
+and activities, <a href="#dfn-valid" class="internalDFN">valid</a> provenance instances <em class="rfc2119" title="must">must</em>
+satisfy <em>ordering constraints</em> between instantaneous events, which are introduced in
+this section. For instance, an entity can only be used after it was
+generated; in other words, an entity's <a title="entity generation
+event" href="#dfn-generation-event" class="internalDFN">generation event</a> precedes any of this
+entity's <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage events</a>. Should this
+ordering constraint be violated, the associated generation and
+usage would not be credible. The rest of this section defines
+the <dfn id="dfn-temporal-interpretation">temporal interpretation</dfn> of provenance instances as a
+set of instantaneous event ordering constraints. </p>
+
+
+<p>To allow for minimalistic clock assumptions, like Lamport
+[<cite><a class="bibref" href="#bib-CLOCK">CLOCK</a></cite>], PROV relies on a notion of relative ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a>,
+without using physical clocks. This specification assumes that a <a href="#dfn-preorder" class="internalDFN">preorder</a> exists between <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a>.
+</p>
+
+
+<p>Specifically, <dfn id="dfn-precedes">precedes</dfn> is a <a href="#dfn-preorder" class="internalDFN">preorder</a>
+between <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a>. A
+constraint of the form
+<span class="name">e1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a> <span class="name">e2</span> means that <span class="name">e1</span>
+happened at the same time as or before <span class="name">e2</span>.
+For symmetry, <dfn id="dfn-follows">follows</dfn> is defined as the
+inverse of <a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>; that is, a constraint of
+the form
+<span class="name">e1</span> follows <span class="name">e2</span> means that <span class="name">e1</span> happened at the same time
+as or after <span class="name">e2</span>. Both relations are
+<a href="#dfn-preorder" class="internalDFN">preorder</a>s, meaning that they are <a href="#dfn-reflexive" class="internalDFN">reflexive</a> and
+<a href="#dfn-transitive" class="internalDFN">transitive</a>. Moreover, we sometimes consider <em>strict</em> forms of these
+orders: we say <span class="name">e1</span> <dfn id="dfn-strictly-precedes">strictly precedes</dfn> <span class="name">e2</span> to indicate that <span class="name">e1</span>
+happened before <span class="name">e2</span>, but not at the same time. This is a
+<a href="#dfn-transitive" class="internalDFN">transitive</a>, <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> relation. </p>
+
+
+<p>PROV also allows for time observations to be inserted in
+specific provenance statements, for each of the five kinds of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a> introduced in
+this specification. Times in provenance records arising from
+different sources might be with respect to different timelines
+(e.g. different time zones) leading to apparent inconsistencies. For
+the purpose of checking ordering constraints, the times associated
+with events are irrelevant; thus, there is no inference that time ordering
+implies event ordering, or vice versa. However, an application <em class="rfc2119" title="may">may</em> flag time values
+that appear inconsistent with the event ordering as possible
+inconsistencies. When generating provenance, an application <em class="rfc2119" title="should">should</em>
+use a consistent timeline for related PROV statements within an
+instance.</p>
+
+
+<p> A typical ordering constraint is as follows.</p>
+
+ <div class="constraint-example" id="ordering-example"><div class="ruleTitle"><a class="internalDFN" href="#ordering-example">Constraint-example NNN (ordering-example)</a></div>
+ <p><span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span> <span class="conditional">THEN</span> <span class="name">evt1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a>/<a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a> <span class="name">evt2</span>. </p></div>
+ <p>
+ The conclusion of an ordering constraint is either <a href="#dfn-precedes" class="internalDFN">precedes</a>
+ or <a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a>. One way to check
+ ordering constraints is to
+ generate all <a href="#dfn-precedes" class="internalDFN">precedes</a> and <a title="precedes" href="#dfn-precedes" class="internalDFN">strictly
+ precedes</a>
+ relationships arising from the ordering constraints to form a directed graph, with edges marked <a href="#dfn-precedes" class="internalDFN">precedes</a> or
+ <a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a>, and check that there is no cycle
+ containing a <a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a> edge.
+ </p>
+
+
+
+<!-- Constraint template:
+<span class="conditional">IF</span>
+<span class="name">blah</span>
+and
+<span class="name">blah</span>
+<span class="conditional">THEN</span>
+<span class="name">XX</span>
+<a>precedes</a>
+<span class="name">YY</span>.
+-->
+
+<section id="activity-constraints">
+<h4><span class="secno">6.2.1 </span>Activity constraints</h4>
+
+<p>
+This section specifies ordering constraints from the perspective of
+the <a href="#lifetime" class="internalDFN">lifetime</a> of an activity. An activity starts, then during
+its lifetime can use, generate or invalidate entities, communicate
+ with, start, or end
+other
+activities, or be associated with agents, and finally it ends. The following constraints amount to
+checking that all of the events associated with an activity take place
+within the activity's lifetime, and the start and end events mark the
+start and endpoints of its lifetime.
+</p>
+
+<p><a href="#ordering-activity" class="fig-ref">Figure 3</a> summarizes the ordering
+ constraints on activities in a
+graphical manner. For this and subsequent figures, an event time line points to the
+right. Activities are represented by rectangles, whereas entities are
+represented by circles. Usage, generation and invalidation are
+represented by the corresponding edges between entities and
+activities. The five kinds of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a> are represented by vertical
+dotted lines (adjacent to the vertical sides of an activity's
+rectangle, or intersecting usage and generation edges). The ordering
+constraints are represented by triangles: an occurrence of a triangle between two <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> vertical dotted lines represents that the event denoted by the left
+line precedes the event denoted by the right line.</p>
+
+<!--
+<div class="note"> Miscellaneous suggestions about figures
+ (originally from Tim Lebo): NOW ADDRESSED
+<ul>
+ <li>
+ I think it would help if the "corresponding edges between entities and activities" where the same visual style as the vertical line marking the time the Usage, generation and derivation occurred. A matching visual style provides a Gestalt that matches the concept. I am looking at subfigures b and c in 5.2. </ul>
+ </div>
+
+ -->
+
+ <div style="text-align: center;">
+
+<span class="figure" id="ordering-activity">
+<img src="images/constraints/ordering-activity.png" alt="constraints between events">
+<br>
+<span class="figcaption" id="ordering-activity-fig">Figure 3<sup><a class="internalDFN" href="#ordering-activity-fig"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering constraints for activities</span> <!-- <b>Figure 3:</b> -->
+</span>
+</div>
+
+
+
+<hr>
+
+<p id="start-precedes-end_text">
+The existence of an activity implies that the <a href="#dfn-start-event" class="internalDFN">activity start
+event</a> always <a href="#dfn-precedes" class="internalDFN">precedes</a> the corresponding <a href="#dfn-end-event" class="internalDFN">activity end
+event</a>. This is illustrated by
+<a href="#ordering-activity" class="fig-ref">Figure 3</a>
+(a) and expressed by <a class="rule-ref" href="#start-precedes-end"><span>Constraint 30 (start-precedes-end)</span></a>.</p>
+
+<div class="constraint" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint 30 (start-precedes-end)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">wasStartedBy(start; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+</p>
+</div>
+<p>
+
+</p><hr>
+
+<p id="start-start-ordering_text">
+If an activity is started by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two start
+events that start the same activity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other.
+</p>
+<div class="constraint" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint 31 (start-start-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasStartedBy(start1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasStartedBy(start2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">start2</span>.
+ </p>
+</div>
+
+<hr>
+
+<p id="end-end-ordering_text">
+If an activity is ended by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two end
+events that end the same activity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other, that is, they are simultaneous.
+</p>
+<div class="constraint" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint 32 (end-end-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasEndedBy(end1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">end1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </p>
+</div>
+
+<hr>
+
+<p id="usage-within-activity_text">A usage implies ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since the <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage event</a> had to occur during the associated activity. This is
+illustrated by <a href="#ordering-activity" class="fig-ref">Figure 3</a> (b) and expressed by <a class="rule-ref" href="#usage-within-activity"><span>Constraint 33 (usage-within-activity)</span></a>.</p>
+
+<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="conditional">IF</span>
+<span class="name">wasStartedBy(start; a,_e1,_a1,_t1,_attrs1)</span>
+ and
+<span class="name">used(use; a,_e2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">use</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">used(use; a,_e1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">use</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+ </li>
+ </ol>
+</div>
+
+<p>
+
+</p><hr>
+
+
+<p id="generation-within-activity_text">A generation implies ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since the <a title="entity generation event" href="#dfn-generation-event" class="internalDFN">generation event</a> had to occur during the associated activity. This is
+illustrated by <a href="#ordering-activity" class="fig-ref">Figure 3</a> (c) and expressed by <a class="rule-ref" href="#generation-within-activity"><span>Constraint 34 (generation-within-activity)</span></a>.</p>
+
+<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="conditional">IF</span>
+<span class="name">wasStartedBy(start; a,_e1,_a1,_t1,_attrs1)</span>
+ and
+<span class="name">wasGeneratedBy(gen; _e2,a,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; _e,a,_t,_attrs)</span>
+and
+<span class="name">wasEndedBy(end; a,_e1,_a1,_t1,_attrs1)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+ </li>
+ </ol>
+</div>
+
+<p>
+
+</p><hr>
+<p id="wasInformedBy-ordering_text">
+Communication between two activities <span class="name">a1</span>
+and <span class="name">a2</span> also implies ordering
+of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since some entity must
+have been generated by the former and used by the latter, which
+implies that the start event of <span class="name">a1</span> cannot
+follow the end event of <span class="name">a2</span>. This is
+illustrated by
+<a href="#ordering-activity" class="fig-ref">Figure 3</a>
+(d) and expressed by <a class="rule-ref" href="#wasInformedBy-ordering"><span>Constraint 35 (wasInformedBy-ordering)</span></a>.</p>
+
+<div class="constraint" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint 35 (wasInformedBy-ordering)</a></div>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasInformedBy(_id; a2,a1,_attrs)</span>
+and
+<span class="name">wasStartedBy(start; a1,_e1,_a1',_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end; a2,_e2,_a2',_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+</p>
+</div>
+<p>
+
+<!-- OLD; delete
+<hr />
+
+<p id='wasStartedByActivity-ordering_text'>Start
+of <span class="name">a2</span> by
+activity <span class="name">a1</span> also implies ordering
+of <a title="instantaneous event">events</a>,
+since <span class="name">a1</span> must have been active
+before <span class="name">a2</span> started. This is illustrated by
+<a href="#ordering-activity">Figure 3</a>
+(e) and expressed by <a class="rule-ref"
+href="#wasStartedByActivity-ordering"><span>TBD</span></a>.</p>
+
+
+<div class='constraint' id='wasStartedByActivity-ordering'>
+ <span class="conditional">IF</span>
+<span class="name">wasStartedBy(start2; a2,-,a1,-)</span>
+and
+<span class="name">wasStartedBy(start1; a1,-,-,-)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a>strictly precedes</a>
+<span class="name">start2</span>.
+</div>
+-->
+
+</p></section>
+
+<section id="entity-constraints">
+<h4><span class="secno">6.2.2 </span> Entity constraints</h4>
+
+
+<!--
+<div class="note">The figure(s) in this section should have vertical lines with visual styles that match the diagonal arrow that they go with. </div>
+-->
+
+<p>
+As with activities, entities have lifetimes: they are generated, then
+can be used, other entities can be derived from them, and finally they
+can be invalidated. The constraints on these events are
+illustrated graphically in <a href="#ordering-entity" class="fig-ref">Figure 4</a> and
+<a href="#ordering-entity-trigger" class="fig-ref">Figure 5</a>.
+</p>
+
+
+
+<div style="text-align: center;">
+<span class="figure" id="ordering-entity">
+<img src="images/constraints/ordering-entity.png" alt="ordering constraints for entities">
+<br>
+<span class="figcaption" id="ordering-entity-fig">Figure 4<sup><a class="internalDFN" href="#ordering-entity-fig"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering constraints for entities</span></span> <!-- <b>Figure 4:</b> -->
+</div>
+
+<p>
+
+</p><hr>
+
+<p id="generation-precedes-invalidation_text">
+Generation of an entity precedes its invalidation. (This
+follows from other constraints if the entity is used, but it is stated
+explicitly here to cover the case of an entity that is generated and
+invalidated without being used.)</p>
+
+<div class="constraint" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint 36 (generation-precedes-invalidation)</a></div>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.
+</p>
+</div>
+
+
+
+
+<hr>
+
+<p id="generation-precedes-usage_text">
+A usage and a generation for a given entity implies ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since the <a title="entity generation
+event" href="#dfn-generation-event" class="internalDFN">generation event</a> had to precede the <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage event</a>. This is
+illustrated by <a href="#ordering-entity" class="fig-ref">Figure 4</a>(a) and expressed by <a class="rule-ref" href="#generation-precedes-usage"><span>Constraint 37 (generation-precedes-usage)</span></a>.</p>
+
+<div class="constraint" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint 37 (generation-precedes-usage)</a></div>
+<p> <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">used(use; _a2,e,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">use</span>.
+</p>
+</div>
+
+
+<hr>
+
+<p id="usage-precedes-invalidation_text">All usages of an entity precede its invalidation, which is captured by <a class="rule-ref" href="#usage-precedes-invalidation"><span>Constraint 38 (usage-precedes-invalidation)</span></a> (without any explicit graphical representation).</p>
+
+<div class="constraint" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint 38 (usage-precedes-invalidation)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">used(use; _a1,e,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">use</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.</p>
+</div>
+
+
+<hr>
+
+<p id="generation-generation-ordering_text">
+If an entity is generated by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two generation
+events that generate the same entity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other.
+</p>
+<div class="constraint" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint 39 (generation-generation-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen1; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasGeneratedBy(gen2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+ </p>
+</div>
+
+<hr>
+
+<p id="invalidation-invalidation-ordering_text">
+If an entity is invalidated by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two invalidation
+events that invalidate the same entity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other, that is, they are simultaneous.
+</p>
+<div class="constraint" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint 40 (invalidation-invalidation-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasInvalidatedBy(inv1; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">inv1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv2</span>.
+ </p>
+</div>
+
+
+
+<p id="derivation-usage-generation-ordering_text">If there is a
+derivation relationship linking <span class="name">e2</span> and <span class="name">e1</span>, then
+this means that the entity <span class="name">e1</span> had some influence on the entity <span class="name">e2</span>; for this to be possible, some event ordering must be satisfied.
+First, we consider derivations, where the activity and usage are known. In that case, the <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage</a> of <span class="name">e1</span> has to precede the <a title="entity generation
+event" href="#dfn-generation-event" class="internalDFN">generation</a> of <span class="name">e2</span>.
+This is
+illustrated by <a href="#ordering-entity-fig">Figure 4</a> (b) and expressed by <a class="rule-ref" href="#derivation-usage-generation-ordering"><span>Constraint 41 (derivation-usage-generation-ordering)</span></a>.</p>
+
+
+<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>
+ <p>
+ In this constraint, <span class="name">_a</span>, <span class="name">gen2</span>, <span class="name">use1</span> <em class="rfc2119" title="must not">must not</em> be placeholders.</p>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasDerivedFrom(_d; _e2,_e1,_a,gen2,use1,_attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">use1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+</p>
+</div>
+<p>
+</p><hr>
+
+<p id="derivation-generation-generation-ordering_text">
+When the activity, generation or usage is unknown, a similar constraint exists, except that the constraint refers to its
+generation event, as
+illustrated by <a href="#ordering-entity-fig">Figure 4</a> (c) and expressed by <a class="rule-ref" href="#derivation-generation-generation-ordering"><span>Constraint 42 (derivation-generation-generation-ordering)</span></a>.</p>
+
+<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>
+ <p>
+In this constraint, any of <span class="name">_a</span>, <span class="name">_g</span>, <span class="name">_u</span> <em class="rfc2119" title="may">may</em> be placeholders.</p>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasDerivedFrom(_d; e2,e1,_a,_g,_u,attrs)</span>
+ and
+<span class="name">wasGeneratedBy(gen1; e1,_a1,_t1,_attrs1)</span>
+ and
+<span class="name">wasGeneratedBy(gen2; e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a>
+<span class="name">gen2</span>.
+</p>
+ </div>
+
+<div class="remark">
+ <p>This constraint requires the derived
+ entity to be generated strictly following the generation of the
+ original entity. This follows from the [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] definition of
+ derivation: <em>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</em>, thus
+ the derived entity must be newer than the original entity.</p>
+ <p>The event ordering is between generations of <span class="name">e1</span>
+and <span class="name">e2</span>, as opposed to derivation where usage is known,
+which implies ordering between the usage of <span class="name">e1</span> and
+generation of <span class="name">e2</span>. </p>
+</div>
+
+<hr>
+
+<p id="wasStartedBy-ordering_text">
+The entity that triggered the start of an activity must exist before the activity starts.
+This is
+illustrated by <a href="#ordering-entity-trigger" class="fig-ref">Figure 5</a>(a) and expressed by <a class="rule-ref" href="#wasStartedBy-ordering"><span>Constraint 43 (wasStartedBy-ordering)</span></a>.</p>
+
+
+<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="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasStartedBy(start; _a,e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">start</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasStartedBy(start; _a,e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.
+ </li>
+ </ol>
+</div>
+
+<hr>
+
+<p id="wasEndedBy-ordering_text"> Similarly, the entity that triggered
+the end of an activity must exist before the activity ends, as
+illustrated by
+<a href="#ordering-entity-trigger" class="fig-ref">Figure 5</a>(b).</p>
+
+
+<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="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+ <span class="name">wasEndedBy(end; _a,e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasEndedBy(end; _a,e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">end</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.
+ </li>
+ </ol>
+</div>
+
+<div style="text-align: center; ">
+<span class="figure" id="ordering-entity-trigger">
+<img src="images/constraints/ordering-entity-trigger.png" alt="ordering constraints for trigger entities">
+<br>
+<span class="figcaption" id="ordering-entity-trigger-fig">Figure 5<sup><a class="internalDFN" href="#ordering-entity-trigger-fig"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering constraints for trigger entities</span> <!-- <b>Figure 5:</b> -->
+</span>
+</div>
+
+<hr>
+<p id="specialization-generation-ordering_text">
+If an entity is a specialization of another, then the more
+specific entity must have been generated after the
+less specific entity was generated.
+</p>
+<div class="constraint" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint 45 (specialization-generation-ordering)</a></div>
+ <p>
+<span class="conditional">IF</span> <span class="name">specializationOf(e2,e1)</span> and <span class="name">wasGeneratedBy(gen1; e1,_a1,_t1,_attrs1)</span> and
+ <span class="name">wasGeneratedBy(gen2; e2,_a2,_t2,_attrs2)</span>
+ <span class="conditional">THEN</span> <span class="name">gen1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a> <span class="name">gen2</span>.
+</p></div>
+
+<p>
+
+</p><hr>
+<p id="specialization-invalidation-ordering_text">
+Similarly, if an entity is a specialization of another entity, and
+then
+the invalidation event of the more specific entity precedes that of
+the less specific entity.
+</p><div class="constraint" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint 46 (specialization-invalidation-ordering)</a></div>
+ <p>
+<span class="conditional">IF</span> <span class="name">specializationOf(e1,e2)</span> and
+ <span class="name">wasInvalidatedBy(inv1; e1,_a1,_t1,_attrs1)</span> and
+ <span class="name">wasInvalidatedBy(inv2; e2,_a2,_t2,_attrs2)</span>
+ <span class="conditional">THEN</span> <span class="name">inv1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a> <span class="name">inv2</span>.
+</p>
+ </div>
+
+</section>
+
+<section id="agent-constraints">
+<h4><span class="secno">6.2.3 </span> Agent constraints</h4>
+
+<p> Like entities and activities, agents have lifetimes that follow a
+familiar pattern. An agent that is also an entity can be generated
+and invalidated; an agent that is also an activity can be started or
+ended. During its lifetime, an agent can participate in interactions
+such as starting or ending other activities, association with an
+activity, attribution, or delegation.
+
+</p> <p>Further constraints associated with agents appear in <a href="#ordering-agents">Figure 6</a> and are discussed below.</p>
+
+<div style="text-align: center;">
+<span class="figure" id="ordering-agents-fig">
+<img src="images/constraints/ordering-agents.png" alt="ordering constraints for agents">
+<br>
+<span class="figcaption" id="ordering-agents">Figure 6<sup><a class="internalDFN" href="#ordering-agents"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering
+ constraints for agents</span> <!--<b>Figure 6:</b> -->
+</span>
+</div>
+
+<hr>
+
+
+<p id="wasAssociatedWith-ordering_text">An activity that was
+associated with an agent must have some overlap with the agent. The
+agent <em class="rfc2119" title="must">must</em> have been generated (or started), or <em class="rfc2119" title="must">must</em> have become
+associated with the activity, after the activity start: so, the agent <em class="rfc2119" title="must">must</em> exist before the activity end. Likewise, the agent may be destructed (or ended), or may terminate its association with the activity, before the activity end: hence, the agent invalidation (or end) is required to happen after the activity start.
+This is illustrated by <a href="#ordering-agents">Figure 6</a> (a) and expressed by <a class="rule-ref" href="#wasAssociatedWith-ordering"><span>Constraint 47 (wasAssociatedWith-ordering)</span></a>.</p>
+
+
+
+<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="name">_pl</span> <em class="rfc2119" title="may">may</em> be
+ a placeholder <span class="name">-</span>.
+ </p><ol> <li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv2; ag,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasGeneratedBy(gen1; ag,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; ag,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; ag,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li>
+ </ol>
+</div>
+
+
+<p>
+
+</p><hr>
+
+<p id="wasAttributedTo-ordering_text">An agent to which an entity was attributed, <em class="rfc2119" title="must">must</em> exist before this entity was generated.
+This is
+illustrated by <a href="#ordering-agents">Figure 6</a> (b) and expressed by <a class="rule-ref" href="#wasAttributedTo-ordering"><span>Constraint 48 (wasAttributedTo-ordering)</span></a>.</p>
+
+
+
+
+<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="conditional">IF</span>
+<span class="name">wasAttributedTo(_at; e,ag,_attrs)</span>
+and
+<span class="name">wasGeneratedBy(gen1; ag,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasGeneratedBy(gen2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAttributedTo(_at; e,ag,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; ag,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasGeneratedBy(gen2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+ </li>
+ </ol>
+</div>
+
+<p>
+</p><hr>
+
+<p id="actedOnBehalfOf-ordering_text">For delegation, the responsible agent has to precede or have some overlap with the subordinate agent.</p>
+
+
+<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="conditional">IF</span>
+<span class="name">actedOnBehalfOf(_del; ag2,ag1,_a,_attrs)</span>
+and
+<span class="name">wasGeneratedBy(gen1; ag1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv2; ag2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">actedOnBehalfOf(_del; ag2,ag1,_a,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; ag1,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; ag2,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li>
+ </ol>
+
+</div>
+
+</section>
+
+</section> <!--event-ordering-constraints-->
+
+
+
+<section id="type-constraints">
+<h3><span class="secno">6.3 </span>Type Constraints</h3>
+
+<p id="typing_text">The following rules assign types to identifiers
+based on their use within statements.
+The function <span class="name">typeOf</span> gives the set of types denoted by an identifier.
+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>.
+</p>
+
+
+
+
+<p>
+ For any identifier <span class="name">id</span>, <span class="name">typeOf(id)</span> is a subset of {<span class="name">'entity'</span>, <span class="name">'activity'</span>, <span class="name">'agent'</span>, <span class="name">'prov:Collection'</span>, <span class="name">'prov:EmptyCollection'</span>}.
+For identifiers that do not have a type, <span class="name">typeOf</span> gives the empty set.
+ Identifiers can have more than one type, because of subtyping
+ (e.g. <span class="name">'prov:EmptyCollection'</span> is a subtype of <span class="name">'prov:Collection'</span>) or because certain types are not
+ disjoint (such as <span class="name">'agent'</span> and <span class="name">'entity'</span>). The set of types
+ does not reflect all of the distinctions among objects, only those
+ relevant for checking validity. In particular, a subtype such as <span class="name">'plan'</span> is omitted, and statements such as <span class="name">wasAssociatedWith</span> that have plan parameters only check that these parameters are entities.
+</p>
+
+<p>To check if a PROV instance satisfies type constraints, one obtains the types of identifiers by application of
+<a class="rule-ref" href="#typing"><span>Constraint 50 (typing)</span></a>
+and check that none of the impossibility constraints
+<a class="rule-ref" href="#entity-activity-disjoint"><span>Constraint 55 (entity-activity-disjoint)</span></a> and
+<a class="rule-ref" href="#membership-empty-collection"><span>Constraint 56 (membership-empty-collection)</span></a> are
+ violated as a result.</p>
+
+
+<div class="constraint" id="typing"><div class="ruleTitle"><a class="internalDFN" href="#typing">Constraint 50 (typing)</a></div>
+
+
+<ol>
+<li>
+<span class="conditional">IF</span>
+ <span class="name">entity(e,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span>.
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">agent(ag,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'agent' ∈ typeOf(ag)</span>.
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">activity(a,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">used(u; a,e,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span> AND
+<span class="name">'entity' ∈ typeOf(e)</span>.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasGeneratedBy(gen; e,a,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">wasInformedBy(id; a2,a1,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a2)</span> AND
+<span class="name">'activity' ∈ typeOf(a1)</span>.
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">wasStartedBy(id; a2,e,a1,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a2)</span> AND
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a1)</span>.
+
+
+
+</li><li>
+
+
+<span class="conditional">IF</span>
+ <span class="name">wasEndedBy(id; a2,e,a1,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a2)</span> AND
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a1)</span>.
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasInvalidatedBy(id; e,a,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(id; e2, e1, a, g2, u1, attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+ In this constraint, <span class="name">a</span>, <span class="name">g2</span>, and <span class="name">u1</span> <em class="rfc2119" title="must not">must not</em> be placeholders.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(id; e2, e1, -, -, -, attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span>.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasAttributedTo(id; e,ag,attr)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'agent' ∈ typeOf(ag)</span>.
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasAssociatedWith(id; a,ag,pl,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span> AND
+<span class="name">'agent' ∈ typeOf(ag)</span> AND
+<span class="name">'entity' ∈ typeOf(pl)</span>. In this
+constraint, <span class="name">pl</span> <em class="rfc2119" title="must not">must not</em> be a placeholder.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasAssociatedWith(id; a,ag,-,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span> AND
+<span class="name">'agent' ∈ typeOf(ag)</span>.
+
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">actedOnBehalfOf(id; ag2,ag1,a,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'agent' ∈ typeOf(ag2)</span> AND
+<span class="name">'agent' ∈ typeOf(ag1)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">alternateOf(e2, e1)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span>.
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">specializationOf(e2, e1)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span>.
+
+
+<!--
+<li>
+<span class='conditional'>IF</span>
+ <span class='name'>mentionOf(e2,e1,b)</span>
+<span class='conditional'>THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span> AND
+<span class="name">'entity' ∈ typeOf(b)</span>.
+-->
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">hadMember(c,e)</span>
+<span class="conditional">THEN</span>
+<span class="name">'prov:Collection' ∈ typeOf(c)</span> AND
+<span class="name">'entity' ∈ typeOf(c)</span> AND
+<span class="name">'entity' ∈ typeOf(e)</span>.
+
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">entity(c,[prov:type='prov:EmptyCollection'])</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(c)</span> AND
+<span class="name">'prov:Collection' ∈ typeOf(c)</span>AND
+<span class="name">'prov:EmptyCollection' ∈ typeOf(c)</span>.
+
+</li></ol>
+</div>
+
+</section> <!--type-constraints-->
+
+<section id="impossibility-constraints">
+<h3><span class="secno">6.4 </span>Impossibility constraints</h3>
+
+<p> Impossibility constraints require that certain patterns of
+statements never appear in <a href="#dfn-valid" class="internalDFN">valid</a> PROV instances. Impossibility
+constraints have the following general form:
+</p>
+
+<div class="constraint-example" id="impossible-example"><div class="ruleTitle"><a class="internalDFN" href="#impossible-example">Constraint-example NNN (impossible-example)</a></div>
+ <p><span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span> <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+
+<p> Checking an impossibility constraint on instance <span class="math">I</span> means checking whether there is
+any way of matching the pattern <span class="name">hyp<sub>1</sub></span>, ..., <span class="name">hyp<sub>n</sub></span>. If there
+is, then checking the constraint on <span class="math">I</span> fails (which implies that
+<span class="math">I</span> is invalid).
+
+
+</p><hr>
+
+<p id="impossible-unspecified-derivation-generation-use_text">
+A derivation with unspecified activity <span class="name">wasDerivedFrom(id;e1,e2,-,g,u,attrs)</span> represents a derivation that
+ takes one or more steps, whose activity, generation and use events
+ are unspecified. It is forbidden to specify a generation or use
+ event without specifying the activity.</p>
+
+ <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>
+<p> In the following rules, <span class="name">g</span> and <span class="name">u</span> <em class="rfc2119" title="must not">must not</em> be <span class="name">-</span>.</p>
+ <ol>
+ <li> <span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(_id;_e2,_e1,-,g,-,attrs)</span>
+ <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</li> <li> <span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(_id;_e2,_e1,-,-,u,attrs)</span>
+ <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</li>
+ <li> <span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(_id;_e2,_e1,-,g,u,attrs)</span>
+ <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</li>
+ </ol>
+ </div>
+<hr>
+
+<p id="impossible-specialization-reflexive_text">As noted previously, specialization is a
+ <a href="#dfn-strict-partial-order" class="internalDFN">strict partial order</a>: it is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>.</p>
+
+ <div class="constraint" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint 52 (impossible-specialization-reflexive)</a></div>
+<!--<p>
+ For any entity <span class='name'>e</span>, it is not the case that
+<span class='name'>specializationOf(e,e)</span> holds.</p>-->
+ <p> <span class="conditional">IF</span> <span class="name">specializationOf(e,e)</span> <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+
+
+ <!--
+<hr>
+<div class="note"> This is also a constraint, but follows from
+ irreflexivity and transitivity so it may be omitted.</div>
+
+ <p id="specialization-asymmetric_text"/>
+
+<div class='constraint' id="impossible-specialization-symmetric">
+<p> For any
+ entities <span class='name'>e1</span>, <span
+ class='name'>e2</span>,
+it is not the case that
+ <span class='name'>specializationOf(e1,e2)</span>
+ and
+ <span class='name'>specializationOf(e2,e1)</span>.</p>
+</div>
+-->
+
+
+ <hr>
+
+
+ <p id="impossible-property-overlap_text"> Furthermore, identifiers
+ of basic relationships are disjoint.
+ </p>
+ <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="name">r</span> and <span class="name">s</span>
+ in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>} such that <span class="name">r</span> and <span class="name">s</span>
+ are different relation names, the
+ following constraint holds:
+</p>
+ <p>
+ <span class="conditional">IF</span> <span class="name">r(id; a<sub>1</sub>,...,a<sub>m</sub>)</span> and <span class="name">s(id; b<sub>1</sub>,...,b<sub>n</sub>)</span> <span class="conditional">THEN INVALID</span>.
+ </p>
+ </div>
+
+ <div class="remark">
+ <p>Since <span class="name">wasInfluencedBy</span> is a superproperty of many other
+ properties, it is excluded from the set of properties whose
+ identifiers are required to be pairwise disjoint. The following
+ example illustrates this observation:
+ </p><pre>wasInfluencedBy(id;e2,e1)
+wasDerivedFrom(id;e2,e1)
+</pre>
+<p> This satisfies the disjointness constraint.
+ </p>
+ <p>There is, however, no
+ constraint requiring that every influence relationship is
+ accompanied by a more specific relationship having the same
+ identifier. The following valid example illustrates this observation:
+ </p><pre>wasInfluencedBy(id; e2,e1)
+</pre>
+<p> This is valid; there is no inferrable information about what kind
+ of influence relates <span class="name">e2</span> and <span class="name">e1</span>, other than its identity.
+ </p>
+ </div>
+
+ <p id="impossible-object-property-overlap_text"> Identifiers of entities,
+ agents and activities cannot also be identifiers of properties.
+ </p>
+ <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="name">p</span> in {<span class="name">entity</span>, <span class="name">activity</span>
+ or <span class="name">agent</span>} and for each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+<span class="name">wasInfluencedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasDerivedFrom</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>}, the following
+ impossibility constraint holds:</p>
+
+<p> <span class="conditional">IF</span> <span class="name">p(id,a<sub>1</sub>,...,a<sub>n</sub>)</span> and
+ <span class="name">r(id; b<sub>1</sub>,...,b<sub>n</sub>)</span> <span class="conditional">THEN INVALID</span>.
+ </p>
+ </div>
+
+
+
+
+ <hr>
+ <p id="entity-activity-disjoint_text"> The set of entities and activities are disjoint, expressed by
+ the following constraint:
+ </p>
+ <div class="constraint" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint 55 (entity-activity-disjoint)</a></div>
+<!-- <p>It is not the case that <span class="name">entity(id,_attrs1)</span> and
+<span class="name">activity(id,_t1,_t2,_attrs2)</span>.
+</p>-->
+
+<p>
+ <span class="conditional">IF</span>
+<span class="name">'entity' ∈ typeOf(id)</span> AND
+<span class="name">'activity' ∈ typeOf(id)</span>
+<span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+ <div class="remark">
+ There is no disjointness between entities and agents. This is because one might want to make statements about the provenance of an agent, by making it an entity.
+ For example, one can assert both <span class="name">entity(a1)</span> and <span class="name">agent(a1)</span> in a valid PROV instance.
+ Similarly, there is no disjointness between activities and
+ agents, and one can assert both <span class="name">activity(a1)</span> and <span class="name">agent(a1)</span> in a valid PROV instance.
+ However, one should keep in mind that some specific types of agents may not be suitable as activities.
+ For example, asserting statements such as <span class="name">agent(Bob, [type=prov:Person])</span> and <span class="name">activity(Bob)</span> is discouraged. In these cases, disjointness can be ensured by explicitly asserting the agent as both agent and entity, and applying <a class="rule-ref" href="#entity-activity-disjoint"><span>Constraint 55 (entity-activity-disjoint)</span></a>.
+ </div>
+
+
+ <hr>
+ <p id="membership-empty-collection_text"> An empty collection cannot contain any member, expressed by
+ the following constraint:
+ </p>
+ <div class="constraint" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint 56 (membership-empty-collection)</a></div>
+<p> <span class="conditional">IF</span>
+ <span class="name">hasMember(c,e)</span> and
+<span class="name">'prov:EmptyCollection' ∈ typeOf(c)</span>
+<span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+
+
+
+</section> <!--impossibility-constraints -->
+
+
+</section> <!-- constraints -->
+
+ <section id="normalization-validity-equivalence">
+<!--OddPage--><h2><span class="secno">7. </span>Normalization, Validity, and Equivalence</h2>
+
+
+ <p>We define the notions of <a title="normal form" href="#dfn-normal-form" class="internalDFN">normalization</a>, <a title="valid" href="#dfn-valid" class="internalDFN">validity</a> and
+<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
+ 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 class="name">owl:sameAs</span> as a result of OWL
+ reasoning).
+ </div>
+
+<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>
+
+
+
+ <ol>
+ <li>
+ Apply all definitions to <span class="math">I</span> by replacing each defined statement by its
+ definition (possibly introducing fresh existential variables in
+ the process), yielding an instance <span class="math">I<sub>1</sub></span>.
+ </li>
+ <li>
+ Apply all inferences to <span class="math">I<sub>1</sub></span> by adding the conclusion of each inference
+ whose hypotheses are satisfied and whose entire conclusion does not
+ already hold (again, possibly introducing fresh existential
+ variables), yielding an instance <span class="math">I<sub>2</sub></span>.
+ </li>
+ <li>
+ Apply all uniqueness constraints to <span class="math">I<sub>2</sub></span> by unifying terms or merging statements
+ and applying the resulting substitution to the instance, yielding
+ an instance <span class="math">I<sub>3</sub></span>. If some uniqueness constraint cannot be
+ applied, then normalization fails.
+ </li>
+ <li>If no definitions, inferences, or uniqueness constraints can be applied to instance <span class="math">I<sub>3</sub></span>, then <span class="math">I<sub>3</sub></span> is the
+ normal form of <span class="math">I</span>.</li>
+ <li>Otherwise, the normal form of <span class="math">I</span> is the same as the normal form
+ of <span class="math">I<sub>3</sub></span> (that is, proceed by
+ normalizing <span class="math">I<sub>3</sub></span> at step 1).
+ </li></ol>
+
+<p>Because of the potential interaction among definitions, inferences, and
+ constraints, the above algorithm is iterative. Nevertheless,
+ all of our constraints fall into a class of <a>tuple-generating
+ dependencies</a> and <a>equality-generating dependencies</a> that
+ satisfy a termination condition called <a>weak acyclicity</a> that
+ has been studied in the context of relational databases
+ [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]. Therefore, the above algorithm terminates, independently
+ of the order in which inferences and constraints are applied.
+ <a href="#termination">Appendix A</a> gives a proof that normalization terminates and produces
+ a unique (up to isomorphism) normal form.
+</p>
+
+ <p>
+ A PROV instance is <dfn id="dfn-valid">valid</dfn>
+if its normal form exists and all of
+ the validity constraints succeed on the normal form.
+ The following algorithm can be used to test
+ validity:</p>
+
+<ol>
+ <li>Normalize the instance <span class="math">I</span>, obtaining
+ normal form <span class="math">I'</span>. If
+ normalization fails, then <span class="math">I</span> is not <a href="#dfn-valid" class="internalDFN">valid</a>.
+ </li>
+ <li>Apply all event ordering constraints to <span class="math">I'</span> to build a graph <span class="math">G</span> whose nodes
+ are event identifiers and edges
+ are labeled by "precedes"
+ and "strictly precedes" relationships among events induced by the constraints.</li>
+ <li> Determine whether there is a cycle in <span class="math">G</span> that contains a
+ "strictly precedes" edge. If so, then <span class="math">I</span> is not <a href="#dfn-valid" class="internalDFN">valid</a>.
+ </li>
+ <li>Apply the type constraints <a href="#type-constraints">(section
+ 5.3)</a> to determine whether there are any violations of
+ disjointness. If so, then <span class="math">I</span> is not <a href="#dfn-valid" class="internalDFN">valid</a>.
+ </li><li>
+ Check that none of the impossibility constraints <a href="#impossibility-constraints">(section 5.4)</a> are
+ violated. If any are violated, then <span class="math">I</span> is
+ not <a href="#dfn-valid" class="internalDFN">valid</a>. Otherwise, <span class="math">I</span> is <a href="#dfn-valid" class="internalDFN">valid</a>.
+ </li>
+ </ol>
+
+<p>A normal form of a PROV instance does not exist when a uniqueness
+ constraint fails due to unification or merging failure. </p>
+
+
+
+<p> Two <a href="#dfn-valid" class="internalDFN">valid</a> PROV instances are <dfn id="dfn-equivalent">equivalent</dfn> if they
+ have <a href="#dfn-isomorphic" class="internalDFN">isomorphic</a> normal forms. That is, after applying all possible inference
+rules, the two instances produce the same set of PROV statements,
+up to reordering of statements and attributes within attribute lists,
+ and renaming of existential variables.
+</p>
+ <p>Equivalence can also be checked over pairs of PROV instances that
+ are not necessarily valid, subject to the following rules:
+ </p><ul>
+ <li>If both are valid, then equivalence is
+ defined above.</li>
+ <li>If both are invalid, then equivalence can be
+ implemented in any way provided it is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-symmetric" class="internalDFN">symmetric</a>, and <a href="#dfn-transitive" class="internalDFN">transitive</a>.
+ </li>
+ <li>If one instance is valid and the other is invalid, then the two
+ instances are not equivalent.</li>
+ </ul>
+ <p>
+Equivalence has the following characteristics over valid instances: </p>
+
+<ul>
+ <li>
+ The order of provenance statements is irrelevant to the meaning of
+ a PROV instance. That is, a
+ PROV instance is equivalent to any other instance obtained by
+reordering its statements.
+ </li>
+ <li>The order of attribute-value pairs in attribute lists is
+ irrelevant to the meaning of a PROV statement. That is, a PROV
+ statement carrying attributes is equivalent to any other statement
+ obtained by reordering attribute-value pairs and eliminating
+ duplicate pairs.
+ </li>
+ <li>The particular choices of names of existential variables are irrelevant to the meaning
+ of an instance; that is, the names can be renamed without changing
+ the meaning, as long as different names are always replaced with
+ different names. (Replacing two different names with equal names,
+ however, can
+ change the meaning, so does not preserve equivalence.)</li>
+ <li>
+ Applying inference rules, definitions, and uniqueness constraints preserves equivalence. That is, a <a href="#instance" class="internalDFN">PROV
+ instance</a> is equivalent to the instance obtained by applying any
+ inference rule or definition, or by <a title="unification">unifying</a> two terms or <a href="#dfn-merging" class="internalDFN">merging</a> two statements to
+ enforce a uniqueness constraint.
+ </li>
+ <li>Equivalence is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-symmetric" class="internalDFN">symmetric</a>, and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>. (This is because a valid instance has a unique
+ normal form up to isomorphism [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]). </li>
+</ul>
+
+<p> An application that processes PROV data <em class="rfc2119" title="should">should</em> handle
+equivalent instances in the same way. This guideline is necessarily
+imprecise because "in the same way" is application-specific.
+Common exceptions to this guideline
+include, for example, applications that pretty-print or digitally sign
+provenance, where the order and syntactic form of statements matters. </p>
+
+</section>
+
+<section id="bundle-constraints">
+<h3><span class="secno">7.2 </span>Bundles and Documents</h3>
+
+
+<p>The definitions, inferences, and constraints, and
+the resulting notions of normalization, validity and equivalence,
+work on a single PROV instance. In this
+section, we describe how to deal with general PROV
+documents, possibly including multiple named bundles as well as a
+toplevel instance. Briefly, each bundle is
+handled independently; there is no interaction between bundles from
+the perspective of applying definitions, inferences, or constraints,
+computing normal forms, or checking validity or equivalence.</p>
+
+<p> We model a general PROV document, containing <span class="name">n</span> named bundles
+<span class="name">b<sub>1</sub>...b<sub>n</sub></span>, as a tuple
+<span class="name">(I<sub>0</sub>,[b<sub>1</sub>=I<sub>1</sub>,...,b<sub>n</sub>=I<sub>n</sub>])</span>
+where <span class="name">I<sub>0</sub></span> is the toplevel
+instance, and for each <span class="name">i</span>, <span class="name">I<sub>i</sub></span> is the instance associated with
+bundle <span class="name">b<sub>i</sub></span>. This notation is shorthand for the
+following PROV-N syntax:</p>
+
+<div class="name">
+document<br>
+ I<sub>0</sub><br>
+ bundle b<sub>1</sub><br>
+ I<sub>1</sub><br>
+ endBundle<br>
+ ...<br>
+ bundle b<sub>n</sub><br>
+ I<sub>n</sub><br>
+ endBundle<br>
+endDocument
+</div>
+
+<p> The <a href="#dfn-normal-form" class="internalDFN">normal form</a> of a PROV document
+<span class="name">(I<sub>0</sub>,[b<sub>1</sub>=I<sub>1</sub>,...,[b<sub>n</sub>=I<sub>n</sub>])</span> is <span class="name">(I'<sub>0</sub>,[b<sub>1</sub>=I'<sub>1</sub>,...,b<sub>n</sub>=I'<sub>n</sub>])</span>
+where <span class="name">I'<sub>i</sub></span> is the normal
+form of <span class="name">I<sub>i</sub></span> for each <span class="name">i</span> between 0 and <span class="name">n</span>. </p>
+
+<p>A PROV document is <a href="#dfn-valid" class="internalDFN">valid</a> if each of the bundles <span class="name">I<sub>0</sub></span>,
+..., <span class="name">I<sub>n</sub></span> are valid and none of the bundle identifiers <span class="name">b<sub>i</sub></span> are repeated.</p>
+
+<p>Two (valid) PROV documents <span class="name">(I<sub>0</sub>,[b<sub>1</sub>=I<sub>1</sub>,...,b<sub>n</sub>=I<sub>n</sub>])</span> and
+<span class="name">(I'<sub>0</sub>,[b<sub>1</sub>'=I'<sub>1</sub>,...,b'<sub>m</sub>=I'<sub>m</sub>])</span> are <a href="#dfn-equivalent" class="internalDFN">equivalent</a> if <span class="name">I<sub>0</sub></span> is
+equivalent to <span class="name">I'<sub>0</sub></span> and <span class="name">n = m</span> and
+there exists a permutation <span class="name">P : {1..n} -> {1..n}</span> such that for each <span class="name">i</span>, <span class="name">b<sub>i</sub> =
+b'<sub>P(i)</sub></span> and <span class="name">I<sub>i</sub></span> is equivalent to <span class="name">I'<sub>P(i)</sub></span>.
+</p>
+
+</section> <!-- bundle-constraints-->
+
+
+</section> <!-- normalization, validity, and equivalence -->
+
+
+
+
+
+
+
+
+
+
+
+<section class="glossary" id="glossary">
+ <!--OddPage--><h2><span class="secno">8. </span>Glossary</h2>
+
+ <ul>
+ <li> <dfn id="dfn-antisymmetric">antisymmetric</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-antisymmetric" class="internalDFN">antisymmetric</a> if
+ for any elements <span class="math">x</span>, <span class="math">y</span> of <span class="math">X</span>, if <span class="math">x R y</span> and <span class="math">y R x</span> then <span class="math">x = y</span>.</li>
+ <li> <dfn id="dfn-asymmetric">asymmetric</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-asymmetric" class="internalDFN">asymmetric</a> if
+ <span class="math">x R y</span> and <span class="math">y R x</span> do not hold for any elements <span class="math">x</span>, <span class="math">y</span> of <span class="math">X</span>.</li>
+ <li><dfn id="dfn-equivalence-relation">equivalence relation</dfn>: An equivalence relation is a relation
+ that is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-symmetric" class="internalDFN">symmetric</a>, and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li> <dfn id="dfn-irreflexive">irreflexive</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> if
+ for <span class="math">x R x</span> does not hold for any element <span class="math">x</span> of <span class="math">X</span>.</li>
+ <li><dfn id="dfn-partial-order">partial order</dfn>: A partial order is a relation
+ that is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-antisymmetric" class="internalDFN">antisymmetric</a>, and <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li><dfn id="dfn-preorder">preorder</dfn>: A preorder is a relation that is
+ <a href="#dfn-reflexive" class="internalDFN">reflexive</a> and <a href="#dfn-transitive" class="internalDFN">transitive</a>. (It is not necessarily antisymmetric,
+ meaning there can be cycles of distinct elements <span class="math">x<sub>1</sub> R x<sub>2</sub> R ... R
+ x<sub>n</sub> R x<sub>1</sub>.</span></li>
+ <li> <dfn id="dfn-reflexive">reflexive</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-reflexive" class="internalDFN">reflexive</a> if
+ for any element <span class="math">x</span> of <span class="math">X</span>, we have <span class="math">x R x</span>.</li>
+ <li><dfn id="dfn-strict-partial-order">strict partial order</dfn>: A strict partial order is a
+ relation that is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a>, <a href="#dfn-asymmetric" class="internalDFN">asymmetric</a> and <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li><dfn id="dfn-strict-preorder">strict preorder</dfn>: A strict preorder is a relation
+ that is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> and <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li> <dfn id="dfn-symmetric">symmetric</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-symmetric" class="internalDFN">symmetric</a> if
+ for any elements <span class="math">x</span>, <span class="math">y</span> of <span class="math">X</span>, if <span class="math">x R y</span> then <span class="math">y R x</span>.</li>
+ <li> <dfn id="dfn-transitive">transitive</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-transitive" class="internalDFN">transitive</a> if
+ for any elements <span class="math">x</span>, <span class="math">y</span>, <span class="math">z</span> of <span class="math">X</span>, if <span class="math">x R y</span> and <span class="math">y R z</span> then <span class="math">x R z</span>.</li>
+
+
+ </ul>
+ </section>
+
+
+ <section class="appendix informative" id="termination">
+ <!--OddPage--><h2><span class="secno">A. </span>Termination of normalization</h2><p><em>This section is non-normative.</em></p>
+
+ <p>
+ We will show that normalization terminates, that is, that
+ applying definitions, inferences and uniqueness/key constraints
+ eventually either fails (due to constraint violation) or
+ terminates with a normal form.
+ </p>
+ <p>
+ First, since the inferences and constraints never introduce new
+ defined statements, for the purpose of termination we always expand
+ the definitions first and then consider only normalization of
+ instances in which there are no remaining defined statements.
+ </p>
+ <p>We will prove termination for the simple case where there are no
+ attributes. For the general case, we will show that any
+ nontermination arising from an instance that does involve
+ 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
+ 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
+ in a modular fashion for our system, because there are only a few possible
+ cycles among statements. The following table summarizes seven
+ <em>stages</em> of the inference rules; because there are no
+ cycles among stages, it is sufficient to check weak acyclicity
+ of each stage independently.
+ </p>
+
+ <table border="1">
+ <tbody><tr>
+ <th>Stage #</th>
+ <th>Inference</th>
+ <th>Hypotheses</th>
+ <th>Conclusions</th>
+ </tr>
+ <tr>
+ <td>1</td>
+ <td>19, 20, 21</td>
+ <td class="name">specializationOf</td> <!-- TODO remove mention -->
+ <td class="name">specializationOf, entity</td>
+ </tr>
+ <tr>
+ <td>2</td>
+ <td>7, 8, 13, 14</td>
+ <td class="name">entity, activity, wasAttributedTo, actedOnBehalfOf</td>
+ <td class="name">wasInvalidatedBy, wasStartedBy, wasEndedBy,
+ wasAssociatedWith</td>
+ </tr>
+ <tr>
+ <td>3</td>
+ <td>9, 10</td>
+ <td class="name">wasStartedBy, wasEndedBy</td>
+ <td class="name">wasGeneratedBy</td>
+ </tr>
+ <tr>
+ <td>4</td>
+ <td>11, 12</td>
+ <td class="name">wasDerivedFrom</td>
+ <td class="name">wasGeneratedBy, used, alternateOf</td>
+ </tr>
+ <tr>
+ <td>5</td>
+ <td>16, 17, 18</td>
+ <td class="name">alternateOf, entity</td>
+ <td class="name">alternateOf</td>
+ </tr>
+ <tr>
+ <td>6</td>
+ <td>5, 6</td>
+ <td class="name">wasInformedBy, generated, used</td>
+ <td class="name">wasInformedBy, generated, used</td>
+ </tr>
+ <tr>
+ <td>7</td>
+ <td>15</td>
+ <td>many</td>
+ <td class="name">wasInfluencedBy</td>
+ </tr>
+
+ </tbody></table>
+ <p>
+ For each stage, we show that the stage is weakly acyclic.
+ </p><ul><li>Stages 1 and 5 have no rules with existential quantifiers,
+ so they are weakly acyclic.
+ </li>
+ <li>Stages 2, 3, 4, and 7 have no cycles among the formulas
+ involved, so they are weakly acyclic.
+ </li>
+ <li>For stage 6, we check weak acyclicity using the algorithm
+ in [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>], namely:
+ <ul><li> Given a formula <span class="math">φ(x<sub>1</sub>,...,x<sub>n</sub>) ⇒
+ ∃y<sub>1</sub>,...,y<sub>m</sub>. ψ(x<sub>1</sub>,...,x<sub>n</sub>,y<sub>1</sub>,...,y<sub>m</sub>)</span></li>
+ <li>For every <span class="math">x</span> that occurs in <span class="math">ψ</span>, and for every
+ occurrence of <span class="math">x</span> in <span class="math">φ</span> in position <span class="math">r.i</span>:
+ <ol><li>For every occurrence of <span class="math">x</span> in position <span class="math">s.j</span>, add
+ an edge from <span class="math">r.i</span> to <span class="math">s.j</span> (if it does
+ not already exist). </li>
+ <li>In addition, for every existentially quantified variable <span class="math">y</span>
+ and for every occurrence of <span class="math">y</span> in <span class="math">ψ</span> in position
+ <span class="math">t.k</span>, add a special edge from <span class="math">r.i</span> to <span class="math">t.k</span> (if it does
+ not already exist).
+ </li>
+ </ol>
+ </li>
+ </ul>
+ Weak
+ acyclicity means that there is no cycle involving a special
+ edge in the resulting graph. For the two inferences in stage 6,
+ the following dependency graph witnesses weak
+ acyclicity. The nodes <span class="name">wasGeneratedBy.i</span>,
+ <span class="name">wasInformedBy.i</span>, and <span class="name">used.i</span> denote the <span class="math">i</span>th arguments
+ of the corresponding predicates. The solid edges are ordinary
+ edges, and the dashed edges are <em>special</em> edges.
+ </li>
+ </ul>
+
+
+ <img src="images/constraints/weak-acyclic-6.svg" alt="Graph illustrating weak
+ acyclicity of stage 6">
+
+ <p><b>Termination for instances with attributes.</b>
+ We can translate an instance with attributes to an alternative,
+ purely relational language by introducing a relation
+ <span class="name">attribute(id,a,v)</span> and replacing every statement of the form
+ <span class="name">r(id;a1,...,a<sub>n</sub>,[(k<sub>1</sub>,v<sub>1</sub>),...,(k<sub>m</sub>,v<sub>m</sub>)])</span> with
+ <span class="name">r(id;a1,...,a<sub>n</sub>),attribute(id,k<sub>1</sub>,v<sub>1</sub>),...,attribute(id,k<sub>m</sub>,v<sub>m</sub>)</span>,
+ and similarly for <span class="name">entity</span>, <span class="name">activity</span> and <span class="name">agent</span>
+ attributes. The inference rules can also be translated so as
+ to work on these instances, and a similar argument to
+ the above shows that inference is terminating on instances with
+ explicit attributes. Any infinite
+ sequence of normalization steps on the original instance would
+ lead to an infinite sequence of translated normalization steps
+ on instances with explicit attributes.
+ </p>
+</section>
+
+<section class="appendix" id="changes-since-last-version">
+ <!--OddPage--><h2><span class="secno">B. </span>Changes since last version</h2>
+ <p> Please see the <a href="http://www.w3.org/2011/prov/wiki/ResponsesToPublicComments">
+ Responses to Public Comments on the Last Call Working Draft</a>
+ for more details about the justification of these changes.</p>
+
+<ul>
+ <li>Abstract: clarified that term "validity" is analogous to other
+ notions of validity in Web standards. </li>
+ <li>Added bullet point linking to PROV-SEM under "How to read the
+ PROV family of specifications"</li>
+ <li>Revised sec. 1.2 to clarify terminology (validity), emphasize
+ that any implementation equivalent to the procedural specification
+ is compliant, and clarify that treating "equivalent instances in the
+ same way" is a guideline.</li>
+ <li>Added paragraph to sec 2.4 to clarify the purpose of the section.</li>
+ <li>Sec 2.4 Unification and Merging: changed "merging" to "unification" for terms</li>
+ <li>Sec. 2.4 "Applying definitions, inferences and constraints":
+ Updated merging to unification and added paragraph reinforcing that
+ compliance is algorithm independent</li>
+ <li>Sec. 2.4 "Checking ordering, typing and impossibility
+ constraints": Avoided use of the term "satisfies".</li>
+ <li>Sec. 2.4 "Equivalence and Isomorphism": Extended equivalence to
+ be defined on all instances, valid or not. Removed analogy to RDF.</li>
+ <li>Sec. 2.4 "From Instances to Bundles and Documents": Revised to
+ avoid giving the impression that toplevel instances must be disjoint
+ from bundles; removed reference to RDF.</li>
+ <li>Sec. 3. Clarified and reinforced algorithm independence.</li>
+ <li>Sec. 4. Added clarifying remark about role of definitions.</li>
+ <li>Sec. 4. Avoided reference to RDF, minor clarifications to
+ discussion of existential variables. </li>
+ <li>Sec. 4.1. Spelling correction.</li>
+ <li>Sec. 4.4. Merging -> unification</li>
+ <li>Sec. 5. Merging -> unification terminology change. Added
+ declarative definition of unification. Clarified
+ procedural definition. Removed definition of merging of attribute
+ lists. Updated descriptions of uniqueness and key constraint application.</li>
+ <li>Constraint 23. Renamed e, a, ag to id.</li>
+ <li>Sec. 5.2. Explicitly stated that strictly-precedes is irreflexive.</li>
+ <li>Sec. 5.2. Spelling</li>
+ <li>Sec. 5.2, just before constraint 51: updated text to accurately
+ describe constraint.</li>
+ <li>Sec. 6. Merging -> unification. Updated definition of validity
+ to avoid referring to "satisfies". Explicitly defined isomorphism
+ of instances. Broadened the definition of equivalence so that it is
+ allowed to test arbitrary instances for equivalence. Reinforce the
+ intention of the guideline that applications treat equivalent
+ instances "in the same way".</li>
+ <li>Dropped RDF as a normative reference.</li>
+ <li>Made PROV-DM and PROV-N into normative references.</li>
+ <li>Added "document" and "endDocument" to sec. 6.2.</li>
+ <li>Added sentence of explanation of purpose to beginning.</li>
+ <li>Moved "mention" to a separate note. </li>
+ <li>Added <a href="#concepts">Section 4: Basic Concepts</a>.</li>
+ <li>Miscellaneous final cleanup prior to CR staging.</li>
+</ul>
+
+</section>
+
+<section class="appendix" id="acknowledgements">
+ <!--OddPage--><h2><span class="secno">C. </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. The editors extend special thanks to Ivan Herman (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr>), Paul Groth, Tim Lebo, Simon Miles, Stian Soiland-Reyes, for their thorough reviews.
+ </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 (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="Massachusetts Institute of Technology">MIT</abbr>),
+Jörn Hees (German Research Center for Artificial Intelligence (DFKI) Gmbh),
+Ivan Herman, (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr>),
+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>
+ </section>
+
+
+
+<!-- LocalWords: px DM RL RDF AQ SEM SOTD Definitional wasInformedBy attrs ag
+ -->
+<!-- LocalWords: wasGeneratedBy wasStartedBy gAttr sAttr wasAttributedTo attr
+ -->
+<!-- LocalWords: wasAssociatedWith dAttrs gAttrs wasDerivedFrom uAttrs eAttrs
+ -->
+<!-- LocalWords: wasRevisionOf specializationOf wasQuotedFrom Traceability WD
+ -->
+<!-- LocalWords: tracedTo aAttr actedOnBehalfOf rAttr traceability TODO xsd
+ -->
+<!-- LocalWords: alternateOf wasEndedBy Lamport's timeline subfigure memberOf
+ -->
+<!-- LocalWords: wasStartedByAgent wasAttributedWith derivedByInsertionFrom
+ -->
+<!-- LocalWords: QName derivedByRemovalFrom EmptyCollection wasVersionOf dm
+ -->
+<!-- LocalWords: RecsWD formedness workflow ness operability CSP versa hyp YY
+ -->
+<!-- LocalWords: disambiguating lifecycle conformant minimalistic Lamport fo
+ -->
+<!-- LocalWords: reflexivity antisymmetry timelines timespan WG concl inv TBD
+ -->
+<!-- LocalWords: continuant occurrent modalities toyota womanInRedDress provn
+ -->
+<!-- LocalWords: customerInChairAt manWithGlasses customerInChair irreflexive
+ -->
+<!-- LocalWords: wasStartedByActivity antisymmetric wasInvalidatedBy stmt CHR
+ -->
+<!-- LocalWords: DBCONSTRAINTS formalisms URIs wasInfluencedBy definitional
+ -->
+<!-- LocalWords: wasInvalidated th nontermination implementability att evt
+ -->
+<!-- LocalWords: Irreflexivity mentionOf preorder equalities unsatisfiable De
+ -->
+<!-- LocalWords: Lebo subfigures pre del irreflexivity superproperty typeOf
+ -->
+<!-- LocalWords: disjointness inferrable subtyping subtype subtypes hadMember
+ -->
+<!-- LocalWords: hasMember toplevel sameAs tuple acyclicity isomorphism IRI
+ -->
+<!-- LocalWords: endBundle typeof equational acyclic invertible procedurally
+ -->
+<!-- LocalWords: implementers multi unifier ERCIM Groth Stian Soiland Ilkay
+ -->
+<!-- LocalWords: Altintas Reza B'Far Belhajjame Informatics Coppens IBBT Nies
+ -->
+<!-- LocalWords: Corsar Cresswell Deus DERI Galway satisfiable namespace Kai
+ -->
+<!-- LocalWords: endDocument Dobson Doerr Hellas Eckert EVAIN EBU UER Frew de
+ -->
+<!-- LocalWords: Irini Fundulaki Garijo Universidad Politécnica Vrije Hartig
+ -->
+<!-- LocalWords: Universiteit Hau NCI Sandro Hawke Jörn Hees DFKI Gmbh Hua da
+ -->
+<!-- LocalWords: Hodgson TopQuadrant Trung Huynh Klyne Revelytix Rensselaer
+ -->
+<!-- LocalWords: McCusker McGuinness Paolo Missier Luc Moreau Vinh Edoardo
+ -->
+<!-- LocalWords: Pignotti Paulo Pinheiro Geospatial Retter Runnegar Satya
+ -->
+<!-- LocalWords: Sahoo Schaengold Schutzer FSTC Yogesh Simmhan Theodoridou
+ -->
+<!-- LocalWords: Thibodeau OpenLink Tilmes Zednik Zhao Yuting
+ -->
+<section id="references" class="appendix"><!--OddPage--><h2><span class="secno">D. </span>References</h2><section id="normative-references"><h3><span class="secno">D.1 </span>Normative references</h3><dl class="bibliography"><dt id="bib-PROV-DM">[PROV-DM]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/"><cite>PROV-DM: The PROV Data Model</cite></a>. 11 December 2012, W3C Candidate Recommendation. URL: <a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/">http://www.w3.org/TR/2012/CR-prov-dm-20121211/</a>
+</dd><dt id="bib-PROV-N">[PROV-N]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/"><cite>PROV-N: The Provenance Notation</cite></a>. 11 December 2012, W3C Candidate Recommendation. URL: <a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/">http://www.w3.org/TR/2012/CR-prov-n-20121211/</a>
+</dd><dt id="bib-PROV-O">[PROV-O]</dt><dd>Timothy Lebo; Satya Sahoo; Deborah McGuinness; eds. <a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/"><cite>Provenance Formal Model</cite></a>. 11 December 2012, W3C Candidate Recommendation. URL: <a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/">http://www.w3.org/TR/2012/CR-prov-o-20121211/</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-RFC3987">[RFC3987]</dt><dd>M. Dürst; M. Suignard. <a href="http://www.ietf.org/rfc/rfc3987.txt"><cite>Internationalized Resource Identifiers (IRIs).</cite></a> January 2005. Internet RFC 3987. URL: <a href="http://www.ietf.org/rfc/rfc3987.txt">http://www.ietf.org/rfc/rfc3987.txt</a>
+</dd></dl></section><section id="informative-references"><h3><span class="secno">D.2 </span>Informative references</h3><dl class="bibliography"><dt id="bib-CHR">[CHR]</dt><dd>Thom Frühwirth. <a href="http://constraint-handling-rules.org/"><cite>Constraint Handling Rules</cite></a>. Cambridge University Press URL: <a href="http://constraint-handling-rules.org/">http://constraint-handling-rules.org/</a>
+</dd><dt id="bib-CLOCK">[CLOCK]</dt><dd>L. Lamport. <a href="http://research.microsoft.com/users/lamport/pubs/time-clocks.pdf"><cite>Time, clocks, and the ordering of events in a distributed system</cite></a>. Communications of the ACM 21 (7): 558–565. 1978. URL: <a href="http://research.microsoft.com/users/lamport/pubs/time-clocks.pdf">http://research.microsoft.com/users/lamport/pubs/time-clocks.pdf</a> DOI: doi:10.1145/359545.359563.
+</dd><dt id="bib-DBCONSTRAINTS">[DBCONSTRAINTS]</dt><dd> Ronald Fagin; Phokion G. Kolaitis; Renée J. Miller; Lucian Popa. <a href="http://dx.doi.org/10.1016/j.tcs.2004.10.033"><cite>Data exchange: Semantics and query answering</cite></a>. Theoretical computer science 336(1):89-124 Elsevier URL: <a href="http://dx.doi.org/10.1016/j.tcs.2004.10.033">http://dx.doi.org/10.1016/j.tcs.2004.10.033</a>
+</dd><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/2012/WD-prov-aq-20120619/"><cite>Provenance Access and Query</cite></a>. 19 June 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/">http://www.w3.org/TR/2012/WD-prov-aq-20120619/</a>
+</dd><dt id="bib-PROV-OVERVIEW">[PROV-OVERVIEW]</dt><dd>Editors TBD. <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/"><cite>PROV-OVERVIEW: The PROV Family of Documents</cite></a>. 11 December 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/">http://www.w3.org/TR/2012/WD-prov-overview-20121211/</a>
+</dd><dt id="bib-PROV-PRIMER">[PROV-PRIMER]</dt><dd>Yolanda Gil; Simon Miles; eds. <a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/"><cite>Prov Model Primer</cite></a>. 11 December 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/">http://www.w3.org/TR/2012/WD-prov-primer-20121211/</a>
+</dd><dt id="bib-PROV-SEM">[PROV-SEM]</dt><dd>James Cheney; ed. <a href="http://www.w3.org/2011/prov/wiki/FormalSemanticsStrawman"><cite>Formal Semantics Strawman</cite></a>. 2011, Work in progress. URL: <a href="http://www.w3.org/2011/prov/wiki/FormalSemanticsStrawman">http://www.w3.org/2011/prov/wiki/FormalSemanticsStrawman</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/2012/WD-prov-xml-20121211/"><cite>PROV-XML: The PROV XML Schema</cite></a>. 11 December 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-xml-20121211/">http://www.w3.org/TR/2012/WD-prov-xml-20121211/</a>
+</dd></dl></section></section></body></html>
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+}
+
+</span>
+</style><link rel="stylesheet" href="http://www.w3.org/StyleSheets/TR/W3C-CR"></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>
+
+ </p>
+ <h1 class="title" id="title">Constraints of the Provenance Data Model</h1>
+
+ <h2 id="w3c-candidate-recommendation-11-december-2012"><abbr title="World Wide Web Consortium">W3C<span class="delete"> Working Draft</span></abbr><span class="insert"> Candidate Recommendation</span> 11 <span class="delete">September</span><span class="insert">December</span> 2012</h2>
+ <dl>
+
+ <dt>This version:</dt>
+ <dd><a href="http://www.w3.org/TR/2012/CR-prov-constraints-20121211/"><span class="insert">http://www.w3.org/TR/2012/CR-prov-constraints-20121211/</span></a></dd>
+ <dt><span class="insert">Latest published version:</span></dt>
+ <dd><a href="http://www.w3.org/TR/prov-constraints/"><span class="insert">http://www.w3.org/TR/prov-constraints/</span></a></dd>
+
+
+ <dt><span class="insert">Latest editor's draft:</span></dt>
+ <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html"><span class="insert">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html</span></a></dd>
+
+
+ <dt><span class="insert">Test suite:</span></dt>
+ <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/testcases/process.html"><span class="insert">http://dvcs.w3.org/hg/prov/raw-file/default/testcases/process.html</span></a></dd>
+
+
+ <dt><span class="insert">Implementation report:</span></dt>
+ <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/reports/prov-implementations.html"><span class="insert">http://dvcs.w3.org/hg/prov/raw-file/default/reports/prov-implementations.html</span></a></dd>
+
+
+
+ <dt><span class="insert">Previous version:</span></dt>
+ <dd><a href="http://www.w3.org/TR/2012/WD-prov-constraints-20120911/">http://www.w3.org/TR/2012/WD-prov-constraints-20120911/</a> <a href="diff-c.html"><span class="insert">(colored-coded diff)</span></a></dd><span class="delete">Latest published version:</span><span class="delete">http://www.w3.org/TR/prov-constraints/</span><span class="delete">Latest editor's draft:</span><span class="delete">http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-constraints.html</span><span class="delete">Previous version:</span><span class="delete">http://www.w3.org/TR/2012/WD-prov-constraints-20120503/</span><span class="delete"> (</span><span class="delete">color-coded diffs</span><span class="delete">)</span>
+
+
+ <dt>Editors:</dt>
+ <dd><a href="http://homepages.inf.ed.ac.uk/jcheney">James Cheney</a>, University of Edinburgh</dd>
+<dd><a href="http://www.cs.ncl.ac.uk/people/Paolo.Missier">Paolo Missier</a>, Newcastle University</dd>
+<dd><a href="http://www.ecs.soton.ac.uk/~lavm/">Luc Moreau</a>, University of Southampton</dd>
+
+
+
+ <dt>Author:</dt>
+ <dd><a href="http://users.ugent.be/~tdenies/">Tom De Nies</a>, IBBT - Ghent University</dd>
+
+
+
+ </dl>
+
+
+
+
+
+ <p class="copyright">
+ <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> ©<span class="delete"> 2012-2012 </span><span class="insert">
+ 2012
+
+ </span><a href="http://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup>
+ (<a href="http://www.csail.mit.edu/"><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>,
+ <a href="http://www.ercim.eu/"><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
+ <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved.
+ <abbr title="World Wide Web Consortium">W3C</abbr> <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>
+
+ <section id="abstract" class="introductory"><h2>Abstract</h2>
+<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. PROV-DM is the conceptual data model that forms a
+basis for the <abbr title="World Wide Web Consortium">W3C</abbr> provenance (PROV) family of specifications.
+
+</p>
+
+
+<p> This document defines a subset of PROV instances called
+<i><a href="#dfn-valid" class="internalDFN">valid</a></i> PROV <span class="delete">instances.
+</span><span class="insert">instances, by analogy with notions of
+validity for other Web standards.
+</span>The intent of validation is ensure that a PROV instance represents a<span class="insert">
+consistent</span> history of objects and their interactions <span class="delete">which</span><span class="insert">that</span> is <span class="delete">consistent, and thus </span>safe to
+use for the purpose of logical reasoning and other kinds of analysis.
+Valid PROV instances satisfy
+certain <a>definitions</a>, <a>inferences</a>, and
+<a>constraints</a>. These definitions, inferences, and constraints
+provide a measure of consistency checking for provenance and reasoning
+over provenance. They can also be used to <a title="normal
+form" href="#dfn-normal-form" class="internalDFN">normalize</a> PROV instances to forms that can easily be
+compared in order to determine whether two PROV instances are
+<a href="#dfn-equivalent" class="internalDFN">equivalent</a>. Validity and equivalence are also defined for PROV
+bundles (that is, named instances) and documents (that is, a toplevel
+instance together with zero or more bundles).</p>
+
+</section><section id="sotd" class="introductory"><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>
+<span class="delete">Last Call</span>
+
+<h4 id="prov-family-of-documents"><span class="insert">PROV Family of Documents</span></h4>
+This <span class="insert">document </span>is <span class="delete">the second public release of the PROV-CONSTRAINTS document.
+This is</span><span class="insert">part of the PROV family of documents,</span> a <span class="delete">Last Call Working Draft. The design is not expected</span><span class="insert">set of documents defining various aspects that are necessary</span> to <span class="delete">change significantly, going forward, and now is the key time for external review.</span>
+
+<span class="delete">This specification identifies</span><span class="insert">achieve the vision of inter-operable
+interchange of provenance information in heterogeneous environments such as the Web.</span> <span class="delete">features at
+risk</span><span class="delete"> related to the at-risk Mention feature of</span><span class="insert">These documents are:
+</span><ul>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/"><span class="insert">PROV-OVERVIEW</span></a><span class="insert"> (Note), an overview of the PROV family of documents</span> [<cite><a class="bibref" href="#bib-PROV-OVERVIEW"><span class="insert">PROV-OVERVIEW</span></a></cite><span class="insert">];</span></li>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/"><span class="insert">PROV-PRIMER</span></a><span class="insert"> (Note), a primer for the PROV data model [</span><cite><a class="bibref" href="#bib-PROV-PRIMER"><span class="insert">PROV-PRIMER</span></a></cite><span class="insert">];</span></li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/"><span class="insert">PROV-O</span></a><span class="insert"> (Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [</span><cite><a class="bibref" href="#bib-PROV-O"><span class="insert">PROV-O</span></a></cite><span class="insert">];</span></li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/">PROV-DM</a><span class="insert"> (Recommendation), the PROV data model for provenance [</span><cite><a class="bibref" href="#bib-PROV-DM"><span class="insert">PROV-DM</span></a></cite><span class="delete">]:
+</span><span class="delete">Inference 22 (mention-specialization-inference)</span><span class="delete"> and
+</span><span class="delete">Constraint 31 (unique-mention)</span><span class="delete">.
+These might be removed from PROV-CONSTRAINTS.</span>
+
+<span class="insert">];</span></li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/"><span class="insert">PROV-N</span></a><span class="insert"> (Recommendation), a notation for provenance aimed at human consumption [</span><cite><a class="bibref" href="#bib-PROV-N"><span class="insert">PROV-N</span></a></cite><span class="insert">];</span></li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-constraints-20121211/"><span class="insert">PROV-CONSTRAINTS</span></a><span class="insert">
+(Recommendation), a set of constraints applying to the </span>PROV <span class="delete">Family of Specifications</span><span class="delete">
+This document is part of the PROV family of specifications, a set of specifications defining various aspects that are necessary to achieve the vision of inter-operable
+interchange of provenance information in heterogeneous environments such as the Web. The specifications are:
+</span>
+ <span class="delete">PROV-DM</span><span class="delete">, the PROV </span>data model<span class="delete"> for provenance;</span>
+ <span class="delete">PROV-CONSTRAINTS</span><span class="delete">, a set of constraints applying to the PROV data model </span>
+(this document);</li>
+<li> <span class="delete">PROV-N</span><span class="delete">, a notation</span><a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/"><span class="insert">PROV-AQ</span></a><span class="insert"> (Note), the mechanisms</span> for <span class="insert">accessing and querying </span>provenance <span class="delete">aimed at human consumption;</span><span class="insert">[</span><cite><a class="bibref" href="#bib-PROV-AQ"><span class="insert">PROV-AQ</span></a></cite><span class="insert">]; </span></li>
+<li> <span class="delete">PROV-O</span><span class="delete">,</span><a href="http://www.w3.org/TR/2012/WD-prov-xml-20121211/"><span class="insert">PROV-XML</span></a><span class="insert"> (Note), an XML schema for</span> the PROV <span class="delete">ontology,</span><span class="insert">data model [</span><cite><a class="bibref" href="#bib-PROV-XML"><span class="insert">PROV-XML</span></a></cite><span class="insert">].</span></li>
+
+</ul>
+<h4 id="how-to-read-the-prov-family-of-documentation"><span class="insert">How to read the PROV Family of Documentation</span></h4>
+<ul>
+<li><span class="insert">The primer is the entry point to PROV offering</span> an <span class="delete">OWL2 ontology allowing the mapping of PROV</span><span class="insert">introduction</span> to <span class="delete">RDF;</span>
+ <span class="delete">PROV-AQ</span><span class="delete">, the mechanisms for accessing and querying provenance; </span>
+ <span class="delete">PROV-PRIMER</span><span class="delete">, a primer for the PROV data</span><span class="insert">the provenance</span> model.</li>
+
+<span class="delete">How to read the PROV Family of Specifications</span>
+
+<li>The <span class="delete">primer is the entry point</span><span class="insert">Linked Data and Semantic Web community should focus on PROV-O defining PROV classes and properties specified in an OWL2 ontology. For further details, PROV-DM and PROV-CONSTRAINTS specify the constraints applicable</span> to <span class="delete">PROV offering an introduction to the provenance model.</span>
+<span class="delete">The Linked Data and Semantic Web community should focus on PROV-O
+defining PROV classes and properties specified in an OWL2
+ontology. For further details, PROV-DM and PROV-CONSTRAINTS specify
+the constraints applicable to </span>the data model, and its interpretation.
+
+ </li>
+<li>Developers seeking to retrieve or publish provenance should focus on PROV-AQ.</li>
+<li>Readers seeking to implement other PROV serializations
+should focus on PROV-DM and PROV-CONSTRAINTS. PROV-O and PROV-N offer examples of mapping to RDF and text, respectively.</li>
+</ul>
+
+
+
+
+ <p>
+ This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as a <span class="delete">Last Call Working Draft. </span><span class="insert">Candidate Recommendation.
+
+ </span>This document is intended to become a <abbr title="World Wide Web Consortium">W3C</abbr> 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>).<span class="delete"> The Last Call period ends 10 October</span>
+
+
+ <abbr title="World Wide Web Consortium"><span class="insert">W3C</span></abbr><span class="insert"> publishes a Candidate Recommendation to indicate that the document is believed
+ to be stable and to encourage implementation by the developer community. This
+ Candidate Recommendation is expected to advance to Proposed Recommendation no earlier than
+ 31 January</span> 2012.
+
+ All feedback is welcome.
+ </p>
+
+ <p>
+ Publication as a <span class="delete">Working Draft</span><span class="insert">Candidate Recommendation</span> does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
+ This is a draft document and may be updated, replaced or obsoleted by other documents at
+ any time. It is inappropriate to cite this document as other than work in progress.
+ </p>
+
+
+ <p>
+
+ This <span class="delete">is</span><span class="insert">document was produced by</span> a <span class="delete">Last Call Working Draft and thus the Working Group has determined that this document has satisfied the relevant technical requirements and is sufficiently stable to advance through the Technical Recommendation process.</span><span class="delete">This document was produced by a </span>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>
+
+
+
+
+</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</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="#validation-process-overview-1" 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"><span class="insert">4. </span></span><span class="insert">Basic concepts</span></a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno"><span class="delete">4.</span><span class="insert">5.</span> </span>Definitions and Inferences</a><ul class="toc"><li class="tocline"><a href="#optional-identifiers-and-attributes" class="tocxref"><span class="secno"><span class="delete">4.1</span><span class="insert">5.1</span> </span>Optional Identifiers and Attributes</a></li><li class="tocline"><a href="#entities-and-activities" class="tocxref"><span class="secno"><span class="delete">4.2</span><span class="insert">5.2</span> </span>Entities and Activities</a></li><li class="tocline"><a href="#derivations" class="tocxref"><span class="secno"><span class="delete">4.3</span><span class="insert">5.3</span> </span>Derivations</a></li><li class="tocline"><a href="#agents" class="tocxref"><span class="secno"><span class="delete">4.4</span><span class="insert">5.4</span> </span>Agents</a></li><li class="tocline"><a href="#alternate-and-specialized-entities" class="tocxref"><span class="secno"><span class="delete">4.5</span><span class="insert">5.5</span> </span>Alternate and Specialized Entities</a></li></ul></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno"><span class="delete">5.</span><span class="insert">6.</span> </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno"><span class="delete">5.1</span><span class="insert">6.1</span> </span>Uniqueness Constraints</a></li><li class="tocline"><a href="#event-ordering-constraints" class="tocxref"><span class="secno"><span class="delete">5.2</span><span class="insert">6.2</span> </span>Event Ordering Constraints</a><ul class="toc"><li class="tocline"><a href="#activity-constraints" class="tocxref"><span class="secno"><span class="delete">5.2.1</span><span class="insert">6.2.1</span> </span>Activity constraints</a></li><li class="tocline"><a href="#entity-constraints" class="tocxref"><span class="secno"><span class="delete">5.2.2</span><span class="insert">6.2.2</span> </span> Entity constraints</a></li><li class="tocline"><a href="#agent-constraints" class="tocxref"><span class="secno"><span class="delete">5.2.3</span><span class="insert">6.2.3</span> </span> Agent constraints</a></li></ul></li><li class="tocline"><a href="#type-constraints" class="tocxref"><span class="secno"><span class="delete">5.3</span><span class="insert">6.3</span> </span>Type Constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno"><span class="delete">5.4</span><span class="insert">6.4</span> </span>Impossibility constraints</a></li></ul></li><li class="tocline"><a href="#normalization-validity-equivalence" class="tocxref"><span class="secno"><span class="delete">6.</span><span class="insert">7.</span> </span>Normalization, Validity, and Equivalence</a><ul class="toc"><li class="tocline"><a href="#instances" class="tocxref"><span class="secno"><span class="delete">6.1</span><span class="insert">7.1</span> </span>Instances</a></li><li class="tocline"><a href="#bundle-constraints" class="tocxref"><span class="secno"><span class="delete">6.2</span><span class="insert">7.2</span> </span>Bundles and Documents</a></li></ul></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno"><span class="delete">7.</span><span class="insert">8.</span> </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="#changes-since-last-version" class="tocxref"><span class="secno"><span class="insert">B. </span></span><span class="insert">Changes since last version</span></a></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno"><span class="delete">B.</span><span class="insert">C.</span> </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno"><span class="delete">C.</span><span class="insert">D.</span> </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno"><span class="delete">C.1</span><span class="insert">D.1</span> </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno"><span class="delete">C.2</span><span class="insert">D.2</span> </span>Informative references</a></li></ul></li></ul></section>
+
+
+
+
+
+
+ <section id="introduction">
+ <h2><span class="secno">1. </span>Introduction<br>
+</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.
+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. <span class="insert"> This document defines a form of validation for provenance. </span></p>
+
+
+
+ <section id="conventions">
+<h3><span class="secno">1.1 </span>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" href="#bib-RFC2119">RFC2119</a></cite>].</p>
+
+<p>In this document, logical formulas contain variables written as
+ lower-case identifiers. Some of these variables are written
+ beginning with the underscore character <span class="name">_</span>, by convention, to indicate that they
+ appear only once in the formula. Such variables are
+ provided merely as an aid to the reader. </p>
+
+</section>
+
+
+<section id="purpose">
+
+<h3><span class="secno">1.2 </span>Purpose of this document</h3>
+
+<p>The PROV Data Model, PROV-DM, is a conceptual data model for provenance, which is
+realizable using different representations such as PROV-N and PROV-O.
+A PROV <a><span class="insert">instance</span></a><span class="insert"> is a set of PROV statements.
+A PROV </span><a>document</a> is <span class="delete">a set of PROV statements,
+</span><span class="insert">an instance
+</span>together with zero or more <a>bundles</a>, or named <span class="delete">sets of
+statements.</span><span class="insert">instances.</span> For
+example, a PROV document could be a .provn document, the result
+of a query, a triple store containing PROV statements in RDF, etc.
+<span class="delete">A PROV </span><span class="delete">instance</span><span class="delete"> is a set of PROV statements.
+</span>The
+PROV-DM specification [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] imposes minimal requirements upon
+PROV instances. A <a href="#dfn-valid" class="internalDFN">valid</a> PROV instance corresponds to a
+consistent history of objects and interactions to which logical
+reasoning can be safely applied. <span class="delete">By default, </span>PROV instances need not
+be <a href="#dfn-valid" class="internalDFN">valid</a>. <span class="insert">
+The term </span><a href="#dfn-valid" class="internalDFN"><span class="insert">valid</span></a><span class="insert"> is chosen by analogy with
+notions of validity in other </span><abbr title="World Wide Web Consortium"><span class="insert">W3C</span></abbr><span class="insert"> specifications. This
+terminology differs from the usual meaning of "validity" in logic;
+our notion of validity of a PROV instance/document is closer to
+logical "consistency".
+</span></p>
+
+<p> This document specifies <em>definitions</em> of some
+provenance statements in terms of others, <em>inferences</em> over PROV instances
+that applications <em class="rfc2119" title="may">may</em> employ, and also defines a class of
+<a href="#dfn-valid" class="internalDFN">valid</a> PROV instances by specifying <em>constraints</em> that
+<a href="#dfn-valid" class="internalDFN">valid</a> PROV instances must satisfy. There are four kinds of
+constraints: <em>uniqueness constraints</em>, <em>event ordering
+constraints</em>, <em>impossibility constraints</em>, and <em>type
+constraints</em>.
+Further discussion
+of the semantics of PROV statements, which justifies the definitions, inferences
+and constraints, <span class="insert">and relates the procedural specification approach
+taken here to a declarative specification, </span>can be found in the formal semantics [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>].
+</p>
+
+<p>We define validity and equivalence in terms of a
+concept called <a title="normal form" href="#dfn-normal-form" class="internalDFN">normalization</a>. Definitions, inferences,
+and uniqueness constraints can be applied to <a title="normal
+form" href="#dfn-normal-form" class="internalDFN">normalize</a> PROV instances, and event ordering, typing, and
+impossibility constraints can be checked on the normal form to determine
+<a title="valid" href="#dfn-valid" class="internalDFN">validity</a>. Equivalence of two PROV
+instances can be determined by comparing their normal forms. For PROV
+documents, validity and equivalence amount to checking the validity or
+pairwise equivalence of their respective <span class="delete">documents.</span><span class="insert">instances.</span>
+</p>
+<p>
+This <span class="delete">document outlines</span><span class="insert">specification defines
+validity and equivalence procedurally, via</span> an algorithm<span class="delete"> for validity checking</span> based on
+<a title="normal form" href="#dfn-normal-form" class="internalDFN">normalization</a>. Applications <em class="rfc2119" title="may">may</em> implement
+validity and equivalence checking using normalization, as <span class="delete">suggested
+here, or</span><span class="insert">outlined
+here. Applications </span><em class="rfc2119" title="may"><span class="insert">may</span></em><span class="insert"> also implement validation and equivalence
+checking</span> in
+any other way as long as the same instances or documents are considered valid or
+equivalent, respectively.
+</p>
+
+<p> Checking validity or equivalence are <em class="rfc2119" title="recommended">recommended</em>, but not required, for
+applications compliant with PROV.<span class="delete"> This specification defines how
+validity and equivalence are to be checked, if an application elects
+to support them at all.</span>
+Applications producing provenance <em class="rfc2119" title="should">should</em> ensure that it is
+<a href="#dfn-valid" class="internalDFN">valid</a>, and similarly applications consuming provenance <em class="rfc2119" title="may">may</em> reject provenance that is not <a href="#dfn-valid" class="internalDFN">valid</a>. Applications
+<span class="delete">which</span><span class="insert">that</span> are determining whether PROV instances or documents convey the same
+information <em class="rfc2119" title="should">should</em> check equivalence as specified <span class="delete">here, and </span><span class="insert">here. As a
+guideline, applications </span>should
+
+treat equivalent instances or documents in the same way.<span class="insert"> This is a
+guideline only, because meaning of "in the same way" is
+application-specific. For example, applications that manipulate the syntax of
+PROV instances in particular representations, such as pretty-printing
+or digital signing, have good reasons to treat syntactically
+different, but equivalent, documents differently.</span>
+</p>
+
+</section>
+<section id="structure-of-this-document">
+<h3><span class="secno">1.3 </span>Structure of this document</h3>
+
+<p><a href="#rationale">Section 2</a> gives a brief rationale
+for the definitions, inferences and constraints.
+</p>
+<p>
+<a href="#compliance">Section 3</a> summarizes the
+requirements for compliance with this document, which are specified in
+detail in the rest of the document. </p>
+<p>
+<a href="#concepts"><span class="insert">Section 4</span></a><span class="insert"> defines basic concepts used in the
+rest of the specification. </span></p>
+
+<p> <a href="#inferences">Section <span class="delete">4</span><span class="insert">5</span></a> presents definitions and inferences. Definitions allow replacing shorthand notation in [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>]
+with more explicit and complete statements; inferences allow adding
+new facts representing implicit knowledge about the structure of
+provenance. </p>
+
+<p><a href="#constraints">Section <span class="delete">5</span><span class="insert">6</span></a> presents four kinds of constraints,
+<em>uniqueness</em> constraints that prescribe that certain statements
+must be unique within PROV <a>instances</a>,
+<em>event ordering</em> constraints that require that the records in a
+PROV <a>instance</a> are consistent with a sensible ordering of events
+relating the activities, entities and agents involved,
+<em>impossibility</em> constraints that forbid certain patterns of
+statements in valid PROV instances, and <em>type</em> constraints that
+classify the types of identifiers in valid PROV instances.
+</p>
+
+<p><a href="#normalization-validity-equivalence">Section <span class="delete">6</span><span class="insert">7</span></a> defines the notions
+of <a>validity</a>, <a>equivalence</a> and <a>normalization</a>.
+</p>
+
+
+
+
+</section>
+<section id="audience">
+<h3><span class="secno">1.4 </span> Audience </h3>
+
+<p> The audience for this document is the same as for [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>]: developers
+and users who wish to create, process, share or integrate provenance
+records on the (Semantic) Web. Not all PROV-compliant applications
+need to perform inferences or check validity when processing provenance.
+However, applications that create or transform provenance <em class="rfc2119" title="should">should</em>
+attempt to produce valid provenance, to make it more useful to other
+applications by ruling out nonsensical or inconsistent information.
+</p>
+
+<p>This document assumes familiarity with [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] and employs the
+[<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>] notation.
+</p>
+
+
+</section>
+</section>
+
+<section id="rationale" class="informative">
+<h2><span class="secno">2. </span>Rationale</h2><p><em>This section is non-normative.</em></p>
+<p> This section gives a high-level rationale that provides some
+ further background for the constraints, but does not affect the
+technical content of the rest of the specification.</p>
+
+<section id="entities-activities-and-agents">
+<h3><span class="secno">2.1 </span>Entities, Activities and Agents</h3><p><em><span class="insert">This section is non-normative.</span></em></p>
+<p>
+One of the central challenges in representing provenance information
+is how to deal with change. Real-world objects, information objects
+and Web resources change over time, and the characteristics that make
+them identifiable in a given situation are sometimes subject to change
+as well. PROV allows for things to be described
+in different ways, with different descriptions of their
+state.
+</p>
+
+<p>
+An entity is a thing one wants to provide provenance for
+and whose situation in the world is described by some fixed
+attributes. An entity has a <dfn id="lifetime">lifetime</dfn>,
+defined as the period
+between its <a title="entity generation event" href="#dfn-generation-event" class="internalDFN">generation event</a>
+and its <a title="entity invalidation event" href="#dfn-invalidation-event" class="internalDFN">invalidation event</a>.
+An entity's attributes are established when the entity is
+created and (partially) describe the entity's situation and state
+during the entirety of the entity's lifetime.</p>
+
+<p>
+A different entity (perhaps representing a different user or
+system perspective) may fix other aspects of the same thing, and its provenance
+may be different. Different entities that fix aspects of the same
+thing are called <em>alternates</em>, and the PROV relations of
+<span class="name">specializationOf</span> and <span class="name">alternateOf</span> can be used to link such entities.</p>
+
+<p>Besides entities, a variety of other PROV objects <span class="delete">have</span><span class="insert">and relationships carry</span>
+attributes, including activity, generation, usage, invalidation, start, end,
+communication, attribution, association, delegation, and
+derivation. Each object has an associated duration interval (which may
+be a single time point), and attribute-value pairs for a given object
+are expected to be descriptions that hold for the object's duration.
+</p>
+<p>
+However, the attributes of entities have special meaning because they
+are considered to be fixed aspects
+of underlying, changing things. This motivates constraints on
+<span class="name">alternateOf</span> and <span class="name">specializationOf</span> relating the attribute values of
+different entities.
+</p>
+
+<p>
+In order to describe the provenance of something during an interval
+ over which relevant attributes of the thing are not fixed, a PROV
+ instance would describe multiple entities, each with its own
+ identifier, <a href="#lifetime" class="internalDFN">lifetime</a>, and fixed attributes, and express dependencies between
+ the various entities using <i><a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a></i>. For example, in order to
+ describe the provenance of several versions of a document, involving
+ attributes such as authorship that change over time, one can use
+ different entities for the versions linked by appropriate
+ generation, usage, revision, and invalidation events.
+</p>
+
+<p>There is no assumption that the set of attributes listed in an
+<span class="name">entity</span> statement is complete, nor
+that the attributes are independent or orthogonal of each
+other. Similarly, there is no assumption that the attributes of an
+entity uniquely identify it. Two different entities that present the
+same aspects of possibly different things can have the same
+attributes; this leads to potential ambiguity, which is mitigated through the
+use of identifiers.</p>
+
+<p>An <a>activity</a>'s lifetime is delimited by its <a title="activity start
+event" href="#dfn-start-event" class="internalDFN">start</a> and its <a title="activity end event" href="#dfn-end-event" class="internalDFN">end</a>
+events. It occurs over
+an interval delimited by two <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous
+events</a>. However, an activity statement need not mention start or end time information, because they may not be known.
+An activity's attribute-value pairs are expected to describe the activity's situation during its lifetime.
+</p>
+
+
+
+<p>An activity is not an entity. Indeed, an entity exists in full at
+any point in its lifetime, persists during this interval, and
+preserves the characteristics provided. In
+contrast, an activity is something that occurs, happens, unfolds, or
+develops through time. This
+distinction is similar to the distinction between 'continuant' and
+'occurrent' in logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>].</p>
+
+
+
+</section>
+<section id="events">
+<h3><span class="secno">2.2 </span>Events</h3>
+
+<p> Although time is important for provenance, provenance can be used
+in many different contexts within individual systems and across the
+Web. Different systems may use different clocks which may not be
+precisely synchronized, so when provenance statements are combined by
+different systems, an application may not be able to align the times involved to a
+single global timeline. Hence, PROV is designed to minimize
+assumptions about time. Instead, PROV talks about (identified)
+events. </p>
+
+<p>The PROV data model is implicitly based on a notion of <dfn id="dfn-event">instantaneous event</dfn>s (or just <a title="instantaneous event" href="#dfn-event" class="internalDFN">event</a>s), that mark
+transitions in the world. Events include generation, usage, or
+invalidation of entities, as well as start or end 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 [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>].
+Thus, events help justify <i>inferences</i> on provenance as well as
+<i>validity</i> constraints indicating when provenance is
+ self-consistent.
+
+
+
+</p><p>Five kinds of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous
+events</a> are used in PROV. The <strong>activity start</strong>
+and <strong>activity end</strong> events delimit the beginning and the
+end of activities, respectively. The
+<strong>entity generation</strong>, <strong>entity usage</strong>, and <strong>entity
+invalidation</strong> events apply to entities, and the generation and
+invalidation events delimit the <a href="#lifetime" class="internalDFN">lifetime</a> of an entity. More
+precisely:
+</p>
+
+<p>An <dfn id="dfn-start-event">activity start event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity starts.</p>
+
+<p>An <dfn id="dfn-end-event">activity end event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity ends.</p>
+
+<p>An <dfn id="dfn-generation-event">entity generation event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the final instant of an entity's creation timespan, after which
+it is available for use. The entity did not exist before this event.</p>
+
+
+<p>An <dfn id="dfn-usage-event">entity usage event</dfn> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the first instant of
+an entity's consumption timespan by an activity. The described usage
+had not started before this instant, although the activity could
+potentially have used the same entity at a different time.</p>
+
+
+<p>An <dfn id="dfn-invalidation-event">entity invalidation event</dfn>
+is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that
+marks the initial instant of the destruction, invalidation, or
+cessation of an entity, after which the entity is no longer available
+for use. The entity no longer exists after this event.</p>
+
+</section>
+
+<section id="typing-section">
+<h3><span class="secno">2.3 </span>Types</h3>
+
+<p> As set out in other specifications, the identifiers used in PROV
+documents have associated type information. An identifier can have
+more than one type, reflecting subtyping or allowed overlap between
+types, and so we define a set of types of each identifier, <span class="name">typeOf(id)</span>. Some types are, however,
+required not to overlap (for example, no identifier can describe both
+an entity and an activity).
+In addition, an identifier cannot be used to identify both an object
+(that is, an entity, activity or agent) and a property (that is, a
+named event such as usage, generation, or a relationship such as
+attribution.)
+This specification includes <a href="#type-constraints">disjointness and typing constraints</a> that
+check these requirements. Here, we
+summarize the type constraints in <a href="#typing-table">Table 1</a>.
+</p>
+
+<div id="typing-table-fig">
+ <table id="typing-table" border="1" class="thinborder" style="margin-left: auto; margin-right: auto; border-color: black;">
+<caption id="typing-table-caption">Table 1: Summary of Typing Constraints</caption>
+ <tbody><tr>
+ <th>In relation...</th>
+ <th>identifier</th>
+ <th>has type(s)...</th>
+ </tr>
+
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+ <tr style="text-align: center; ">
+ <td class="name">entity(e,attrs)</td>
+ <td class="name" style="text-align: center; ">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">activity(a,t1,t2,attrs)</td>
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">agent(ag,attrs)</td>
+ <td class="name">ag</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">used(id; a,e,t,attrs)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasGeneratedBy(id; e,a,t,attrs)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasInformedBy(id; a2,a1,attrs)</td>
+ <td class="name">a2</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a1</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasStartedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">a2</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a1</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasEndedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">a2</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a1</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasInvalidatedBy(id; e,a,t,attrs)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)</td>
+ <td class="name">e2</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e1</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">wasAttributedTo(id; e,ag,attr)</td>
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">ag</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">wasAssociatedWith(id; a,ag,pl,attrs)</td>
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">ag</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">pl</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="3" class="name">actedOnBehalfOf(id; ag2,ag1,a,attrs)</td>
+ <td class="name">ag2</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">ag1</td>
+ <td class="name">'agent'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">a</td>
+ <td class="name">'activity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">alternateOf(e1,e2)</td>
+ <td class="name">e1</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e2</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">specializationOf(e1,e2)</td>
+ <td class="name">e1</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e2</td>
+ <td class="name">'entity'</td>
+ </tr>
+
+ <span class="delete">mentionOf(e1,e2,b)</span>
+ <span class="delete">e1</span>
+ <span class="delete">'entity'</span>
+
+
+ <span class="delete">e2</span>
+ <span class="delete">'entity'</span>
+
+
+ <span class="delete">b</span>
+ <span class="delete">'entity'</span>
+
+
+
+ <tr style="text-align: center; ">
+ <td rowspan="2" class="name">hadMember(c,e)</td>
+ <td class="name">c</td>
+ <td class="name">'entity'<br> 'prov:Collection'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">e</td>
+ <td class="name">'entity'</td>
+ </tr>
+ <tr style="text-align: center; ">
+ <td class="name">entity(c,[prov:type='prov:EmptyCollection,...])</td>
+ <td class="name">c</td>
+ <td class="name">'entity'<br> 'prov:Collection' <br> 'prov:EmptyCollection'</td>
+ </tr>
+ </tbody></table>
+ </div>
+
+
+</section>
+<section id="validation-process-overview-1">
+<h3><span class="secno">2.4 </span>Validation Process Overview</h3>
+
+
+ <p>
+ This section collects common concepts and operations that are used
+ throughout the specification, and relates them to background
+ terminology and ideas from logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>], constraint programming
+ [<cite><a class="bibref" href="#bib-CHR">CHR</a></cite>], and database constraints [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]. This section
+ does not attempt to provide a complete introduction to these topics,
+ but it is provided in order to aid readers familiar with one or more
+ of these topics in understanding the specification, and to clarify
+ some of the motivations for choices in the specification to all
+ readers.
+ </p>
+
+
+
+
+ <p><span class="insert">As discussed below, the definitions, inferences and constraints
+can be viewed as pure logical assertions that could be checked in a
+variety of ways. The rest of this document specifies validity and
+equivalence procedurally, that is, in terms of a reference
+implementation based on normalization. Although both declarative and
+procedural specification techniques have advantages, a purely
+declarative specification offers much less guidance for
+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. [</span><cite><a class="bibref" href="#bib-PROV-SEM"><span class="insert">PROV-SEM</span></a></cite><span class="insert">] will provide an alternative,
+declarative characterization of validity and equivalence which could
+be used as a starting point for other implementation strategies. </span></p>
+
+
+
+ <h3 id="constants-variables-and-placeholders">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/prov-n/#prod-QUALIFIED_NAME">qualified names</a> which can be mapped to URIs [<cite><span class="delete">IRI</span><a class="bibref" href="#bib-RFC3987"><span class="insert">RFC3987</span></a></cite>].
+ However, in order to specify
+ constraints over PROV instances, we also need <em>variables</em>
+ that represent unknown identifiers, literals, or placeholders.
+ These variables are similar to those in first-order
+ logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>]. A variable is a symbol that can be replaced by
+ other symbols, including either other variables or constant
+ identifiers, literals, or placeholders. In a few special cases, we
+ also use variables for unknown attribute lists.
+ To help distinguish identifiers and variables, we also term the former 'constant identifiers' to highlight their non-variable nature.
+ </p>
+
+ <p>Several definitions and inferences conclude by saying that some
+ objects exist such that some other formulas hold. Such an inference
+ introduces fresh <a>existential variable</a>s into the instance. An
+ existential variable denotes a fixed object that exists, but its
+ exact identity is unknown. Existential variables can stand for
+ unknown identifiers or literal values only; we do not allow
+ existential variables that stand for unknown attribute lists. </p>
+
+ <p>In particular, many
+ occurrences of the placeholder symbol <span class="name">-</span> stand for unknown
+ objects; these are handled by expanding them to existential
+ variables. Some placeholders, however, indicate the absence of an
+ object, rather than an unknown object. In other words, the
+ placeholder is overloaded, with different meanings in different
+ places.
+ </p>
+ <p>An expression is called a <em>term</em> if it is either a
+ constant identifier, literal, placeholder, or variable. We write
+ <span class="math">t</span> to denote an arbitrary term.
+</p>
+
+
+ <h4 id="substitution-1">Substitution</h4><p><em><span class="insert">This section is non-normative.</span></em></p>
+<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
+ <span class="math">S = [x<sub>1</sub> = t<sub>1</sub>,...,x<sub>n</sub>=t<sub>n</sub>]</span>
+ can be <em>applied</em> to a term <span class="delete">as follows.</span><span class="insert">by replacing occurrences of
+</span><span class="math"><span class="insert">x_i</span></span><span class="insert"> with </span><span class="math"><span class="insert">t_i</span></span><span class="insert">.</span>
+</p>
+<span class="delete">
+ If the term is a variable </span><span class="delete">x</span><span class="delete">i</span><span class="delete">, one of the variables in the
+ domain of </span><span class="delete">S</span><span class="delete">, then </span><span class="delete">S(x</span><span class="delete">i</span><span class="delete">) = t</span><span class="delete">i</span><span class="delete">.
+ </span>
+ <span class="delete">If the term is a constant identifier or literal </span><span class="delete">c</span><span class="delete">, then </span><span class="delete">S(c) = c</span><span class="delete">.
+ </span>
+
+
+
+ <p>
+ In addition, a substitution can be applied to an atomic formula
+ (PROV statement) <span class="math">p(t<sub>1</sub>,...,t<sub>n</sub>)</span> by applying it to each term,
+ that is, <span class="math">S(p(t<sub>1</sub>,...,t<sub>n</sub>)) = p(S(t<sub>1</sub>),...,S(t<sub>n</sub>))</span>. Likewise, a
+ substitution <span class="math">S</span> can be applied to an instance <span class="math">I</span> by applying
+ it to each atomic formula (PROV statement) in <span class="math">I</span>, that is, <span class="math">S(I)
+ = {S(A) | A ∈ I}</span>.
+</p>
+
+
+
+
+
+ <h4 id="formulas">Formulas</h4>
+ <p>
+ For the purpose of constraint checking, we view PROV statements
+ (possibly involving existential variables) as
+ <dfn id="dfn-formulas">formulas</dfn>. An instance is analogous to a "theory" in
+ logic, that is, a set of formulas all thought to describe the same
+ situation. The set can also be thought of a single, large formula:
+ the conjunction of all of the atomic formulas.
+ </p>
+<p>The atomic constraints considered in this specification can be
+ viewed as atomic formulas:</p>
+<ul>
+ <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>
+ </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>.
+ </li>
+ <li>Impossibility constraints employ the conclusion <span class="name">INVALID</span>,
+ which is equivalent to the logical constant <span class="math">False</span>. </li>
+ </ul>
+ <p> Similarly, the definitions, inferences, and constraint rules in this
+ specification can also be viewed as logical formulas, built up out
+ of atomic formulas, logical connectives "and" (∧), "implies" (⇒),
+ and quantifiers "for all" (∀) and "there exists" (∃). For more
+ 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>
+ 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><span class="delete">l</span><span class="insert">p</span></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><span class="delete">l</span><span class="insert">p</span></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><span class="delete">l</span><span class="insert">p</span></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><span class="delete">l</span><span class="insert">p</span></sub> ⇒ C</span>. </li>
+<li>A constraint of the form <span class="conditional">IF</span> <span class="name">A<sub>1</sub> ∧ ... ∧ A<sub><span class="delete">l</span><span class="insert">p</span></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><span class="delete">l</span><span class="insert">p</span></sub> ⇒ False</span>. </li>
+ </ul>
+
+
+ <h4 id="satisfying-definitions-inferences-and-constraints">Satisfying definitions, inferences, and constraints</h4>
+ <p>
+ In logic, a formula's meaning is defined by saying when it is
+ <em>satisfied</em>. We can view
+ definitions, inferences, and constraints as being satisfied or not
+ satisfied in a PROV instance, augmented with information about the constraints.
+ </p>
+ <ol>
+ <li>A logical equivalence as used in a definition is satisfied
+ when the 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> holds, that is, for any substitution of the
+ variables <span class="math">x<sub>1</sub>,....,x<sub>n</sub></span>, formula <span class="math">A</span> and
+ formula <span class="math">∃
+ y<sub>1</sub>...y<sub>m</sub>. B<sub>1</sub> ∧ ... ∧
+ 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">∀
+ x<sub>1</sub>,....,x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧
+ A<sub><span class="delete">l</span><span class="insert">p</span></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
+ the variables <span class="math">x<sub>1</sub>,....,x<sub>n</sub></span>, if <span class="math">A<sub>1</sub> ∧ ... ∧
+ A<sub><span class="delete">l</span><span class="insert">p</span></sub></span> is true, then
+ for some further substitution of terms for variables <span class="math">
+ y<sub>1</sub>...y<sub>m</sub></span>, formula <span class="math">B<sub>1</sub> ∧ ... ∧
+ B<sub>k</sub></span> is also true.</li>
+ <li>A uniqueness, ordering, or typing constraint is satisfied when
+ its associated formula <span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub><span class="delete">l</span><span class="insert">p</span></sub> ⇒ C</span> holds, that is, for any substitution of
+ the variables <span class="math">x<sub>1</sub>,....,x<sub>n</sub></span>, if <span class="math">A<sub>1</sub> ∧ ... ∧
+ A<sub><span class="delete">l</span><span class="insert">p</span></sub></span> is true, then <span class="math">C</span> is
+ also true.</li>
+ <li>An impossibility constraint is satisfied when the formula
+ <span class="math">∀ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub><span class="delete">l</span><span class="insert">p</span></sub> ⇒
+ False</span> holds. This is logically equivalent to <span class="math">∄
+ x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub><span class="delete">l</span><span class="insert">p</span></sub></span>, that is, there exists no
+ substitution for <span class="math">x<sub>1</sub>...x<sub>n</sub></span> making <span class="math">A<sub>1</sub> ∧ ... ∧ A<sub><span class="delete">l</span><span class="insert">p</span></sub></span> true.
+</li></ol>
+
+<h4 id="unification-and-merging"><span class="insert">Unification and </span>Merging</h4>
+
+ <p><em><span class="delete">Merging</span><span class="insert">Unification</span></em> is an operation that takes two terms and compares them to
+ <span class="delete">see if</span><span class="insert">determine whether</span> they<span class="delete"> are equal, or</span> can be made equal by substituting an
+ existential variable with another term. <span class="delete">This operation</span><span class="insert">If so, the result</span> is <span class="insert">such </span>a<span class="delete"> special
+ case of </span><span class="insert">
+ substitution; otherwise, the result is failure. Unification is an
+ essential concept in logic programming and automated reasoning,
+where terms can involve variables, constants and function symbols. In PROV,
+ by comparison, </span>unification<span class="delete">, a common operation in logical
+ reasoning, including logic programming and automated reasoning.
+Merging</span><span class="insert"> only needs to deal with variables,
+ constants and literals.
+</span></p>
+<p><span class="insert">
+Unifying</span> two terms <span class="math">t,t'</span> results in either substitution <span class="math">S</span>
+ such that <span class="math">S(t) = S(t')</span>, or failure indicating that there is no
+ substitution that can be applied to both <span class="math">t</span> and <span class="math">t'</span> to make
+ them equal.
+<span class="insert"> Unification is also used to define an operation on PROV
+ statements called </span><em><span class="insert">merging</span></em><span class="insert">. Merging takes two statements
+ that have equal identifiers, unifies their corresponding term
+ arguments, and combines their attribute lists.
+</span></p>
+
+
+
+ <h4 id="applying-definitions-inferences-and-constraints">Applying definitions, inferences, and constraints</h4>
+<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
+ instance that does satisfy the formula. Definitions, inferences,
+ and uniqueness constraints can be applied to instances:
+</p>
+ <ul>
+ <li>
+ A definition of the form <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>
+ can be applied by searching for any occurrences of <span class="math">A</span> in the instance and adding <span class="math"> B<sub>1</sub>, ..., B<sub>k</sub></span>, generating fresh existential
+ variables <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>, and conversely, whenever there is an
+ occurrence of <span class="math"> B<sub>1</sub>, ..., B<sub>k</sub></span>, adding
+ <span class="math">A</span>.
+ In our setting, the defined formulas <span class="math">A</span> are never used in other
+ formulas, so it is sufficient to replace all occurrences of
+ <span class="math">A</span> with their definitions. The formula <span class="math">A</span> is then redundant, and can be
+ removed from the instance.
+</li>
+<li>An inference of the form <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> 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,
+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
+ variables <span class="math">y<sub>1</sub>,...,y<sub>m</sub></span>.
+</li>
+<li>A uniqueness constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ t
+= t'</span> can be
+ applied by searching for an occurrence <span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> in the instance, and
+ if one is found, <span class="delete">merging</span><span class="insert">unifying</span> the terms <span class="math">t</span> and
+<span class="math">t'</span>. If successful, the resulting
+substitution is applied to the instance; otherwise, the application
+of the uniqueness constraint fails. </li>
+<li>A key constraint can similarly be applied by searching for
+different occurrences of a statement with the same identifier, <span class="delete">merging</span><span class="insert">unifying</span> the
+corresponding parameters of the statements, and concatenating their
+attribute <span class="delete">lists.</span><span class="insert">lists, to form a single statement.</span> The substitutions obtained by <span class="delete">merging</span><span class="insert">unification</span> are applied to
+<span class="insert">the merged statement and the rest of </span>the instance.
+</li>
+ </ul>
+
+ <p>As noted above, uniqueness or key constraint
+ application can <em>fail</em>, if a required <span class="insert">unification or </span>merging step fails. Failure of constraint
+ application means that there is no way to add information to the
+ instance to satisfy the constraint, which in turn implies that the
+ instance is <em>invalid</em>.
+ </p>
+ <p>
+ The process of applying definitions, inferences, and constraints
+ to a PROV instance until all of them are satisfied is similar to
+ what is sometimes
+ called <em>chasing</em> [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>] or <em>saturation</em>
+ [<cite><a class="bibref" href="#bib-CHR">CHR</a></cite>]. We call this process <em>normalization</em>.
+ </p>
+ <p><span class="insert">
+ Although this specification outlines one particular way of
+ performing inferences and checking constraints, based on
+ normalization, implementations can use any other equivalent
+ algorithm. The logical formulas corresponding to the definitions,
+ inferences, and constraints outlined above (and further elaborated
+ in [</span><cite><a class="bibref" href="#bib-PROV-SEM"><span class="insert">PROV-SEM</span></a></cite><span class="insert">]) provides an equivalent specification, and any
+ implementation that correctly checks validity and equivalence (whether it performs normalization or not) complies
+ with this specification.</span>
+ </p>
+
+
+ <h4 id="termination-1">Termination</h4>
+ <p>
+ In general, applying sets of logical formulas of the above
+ definition, inference, and constraint forms is not guaranteed to
+ terminate. A simple example is the inference <span class="math">R(x,y) ⇒ ∃z. R(x,z)
+ ∧R(z,y)</span>, which can be applied to <span class="math">{R(a,b)}</span> to generate an
+ infinite sequence of larger and larger instances. To ensure that
+ normalization, validity, and equivalence are decidable, we require
+ that normalization terminates. There is a great deal of work on termination of the chase in
+ databases, or of sets of constraint handling rules. The termination
+ of the notion of normalization defined in this specification is
+ guaranteed because the definitions, inferences and uniqueness/key
+ constraints correspond to a <em>weakly acyclic</em> set of
+ tuple-generating and equality-generating dependencies, in the
+ terminology of [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]. The termination of the remaining
+ ordering, typing, and impossibility constraints is easy to show. <a href="#termination">Appendix
+ <span class="delete">C</span><span class="insert">A</span></a> gives a proof that the definitions, inferences, and uniqueness
+ and key constraints are weakly acyclic and therefore terminating.
+ </p>
+ <p>
+ There is an important subtlety that is essential to guarantee
+ termination. This specification draws a distinction between knowing
+ that an identifier has type <span class="name">'entity'</span>, <span class="name">'activity'</span>, or <span class="name">'agent'</span>, and having
+ an explicit <span class="name">entity(id)</span>, <span class="name">activity(id)</span>, or <span class="name">agent(id)</span> statement in the instance.
+ For example, focusing on entity statements, we can infer <span class="name">'entity' ∈ typeOf(id)</span> if <span class="name">entity(id)</span> holds in the instance. In contrast, if we only know
+ that <span class="name">'entity' ∈ typeOf(id)</span>, this does not imply that <span class="name">entity(id)</span>
+ holds.
+ </p>
+ <p>
+ This distinction (for both entities and activities) is essential to
+ ensure termination of the inferences, because we allow inferring
+ that a declared <span class="name">entity(id,attrs)</span> has a generation
+ and invalidation event, using
+ <a class="rule-text" href="#entity-generation-invalidation-inference_text"><span>Inference 7 (entity-generation-invalidation-inference)</span></a>.
+ Likewise, for activities, we allow inferring that a declared <span class="name">activity(id,t1,t2,attrs)</span> has a generation
+ and invalidation event, using
+ <a class="rule-text" href="#activity-start-end-inference_text"><span>Inference 8 (activity-start-end-inference)</span></a>. These
+ inferences do not apply to identifiers whose types are known, but for
+ which there is not an explicit entity or activity statement.
+If we strengthened the type
+ inference constraints to add new entity or activity statements for
+ the entities and activities involved in generating or starting other
+ declared entities or activities, then we could keep generating new entities and
+ activities in an unbounded chain into the past (as in the "chicken
+ and egg" paradox). The
+ design adopted here requires that instances explicitly declare the
+ entities and activities that are relevant for validity checking, and only
+ these can be inferred to have invalidation/generation and start/end events. This inference
+ is not supported for identifiers
+that are indirectly referenced in other relations and therefore have
+ type <span class="name">'entity'</span> or <span class="name">'activity'</span>.
+ </p>
+
+
+<div style="text-align: center;">
+<span class="figure" id="fig-figure-1-overview-of-the-validation-process">
+<img src="images/constraints/prov-c.graffle.svg/overview.svg" alt="validation process overview">
+<br>
+<span class="figcaption" id="validation-process-overview">Figure 1<sup><a class="internalDFN" href="#validation-process-overview"><span class="diamond"> ◊:</span></a></sup> Overview of the Validation Process</span>
+</span>
+</div>
+
+
+ <h4 id="checking-ordering-typing-and-impossibility-constraints">Checking ordering, typing, and impossibility constraints</h4>
+ <p>
+ The ordering, typing, and impossibility constraints are checked
+ rather than applied. This means that they do not generate new
+ formulas expressible in PROV, but they do generate basic constraints
+ that might or might not be consistent with each other. Checking
+ such constraints follows a saturation strategy similar to that for normalization:
+ </p>
+ <ol>
+ <li><p>
+ For ordering constraints, we check by generating all of the
+ precedes and strictly-precedes relationships specified by the rules. These can be thought
+ of as a directed graph whose nodes are terms, and whose edges are
+ precedes or strictly-precedes relationships.
+ An ordering constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒
+precedes(t,t')</span> can be applied by searching for occurrences of
+<span class="math"> A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> and for each such match
+adding the atomic formula <span class="math">precedes(t,t')</span> to
+ the instance, and similarly for strictly-precedes constraints. After all such constraints have been checked, and the
+ resulting edges added to the graph, the ordering constraints are
+ violated if there is a cycle in the graph that includes a
+ strictly-precedes edge, and satisfied otherwise.
+ </p>
+</li>
+<li><p>For typing constraints, we check by constructing a function
+ <span class="math">typeOf(id)</span> mapping identifiers to sets of possible types. We
+ start with a function mapping each identifier to the empty set,
+ reflecting no constraints on the identifiers' types. A typing
+ constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒ 'type' ∈ typeOf(id)
+</span> is checked by adjusting the
+ function by adding <span class="name">'type'</span> to <span class="math">typeOf(id)</span> for each conclusion
+ <span class="name">'type' ∈ typeOf(id)</span> of the rule. Typing constraints with
+ multiple conclusions are handled analogously. Once all constraints
+ have been checked in all possible ways, we check that the
+ disjointness constraints hold of the resulting <span class="math">typeOf</span> function.
+ (These are essentially impossibility constraints).
+</p>
+ </li>
+ <li><p>For impossibility constraints, we check by searching for the
+ forbidden pattern that the impossibility constraint describes. Any
+ match of this pattern leads to failure of the constraint checking process.
+An impossibility constraint of the form <span class="math">∀
+x<sub>1</sub>...x<sub>n</sub>. A<sub>1</sub> ∧ ... ∧ A<sub>p</sub> ⇒
+False</span> can be applied by searching for occurrences of
+<span class="math">A<sub>1</sub> ∧ ... ∧ A<sub>p</sub></span> in the instance, and if any
+such occurrence is found, signaling failure.</p>
+ </li>
+ </ol>
+ <p>
+ A normalized instance that <span class="delete">satisfies</span><span class="insert">passes</span> all of the <span class="delete">checked constraints
+ </span><span class="insert">ordering, typing,
+ and impossibility constraint checks
+ </span>is called <a href="#dfn-valid" class="internalDFN">valid</a>. Validity can be, but is not required to be,
+ checked by normalizing and then checking constraints. Any other
+ algorithm that provides equivalent behavior (that is, accepts the
+ same valid instances and rejects the same invalid instances) is allowed.
+ In particular, the checked constraints and the
+ applied definitions, inferences and uniqueness constraints do not
+ interfere with one another, so it is also possible to mix checking
+ and application. This may be desirable in order to detect
+ invalidity more quickly.
+ </p>
+
+
+
+ <h4 id="equivalence-and-isomorphism">Equivalence and Isomorphism</h4>
+ <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
+ logic, if we consider normalized PROV instances with existential
+ variables to represent sets of possible situations, then two normal
+ forms may describe the same situation but differ in inessential
+ details such as the order of statements or of elements of
+ attribute-value lists. To remedy this, we can easily consider
+ instances to be equivalent up to reordering of attributes. However,
+ instances can also be equivalent if they differ only in choice of
+ names of existential variables. Because of this, the appropriate
+ notion of equivalence of normal forms is <em>isomorphism</em>. Two
+ instances <span class="math">I<sub>1</sub></span> and <span class="math">I<sub>2</sub></span> are <em>isomorphic</em> if there is an invertible
+ substitution <span class="math">S</span> mapping existential variables to existential variables such that <span class="math">S(I<sub>1</sub>) = I<sub>2</sub></span>.<span class="delete">
+ This is similar to the notion of equivalence used in [</span><span class="delete">RDF</span><span class="delete">], where
+ blank nodes play an analogous role to existential variables. </span>
+
+ </p>
+
+<p>Equivalence can be checked by normalizing instances, checking that
+ both instances are valid, then
+ testing whether the two normal forms are isomorphic. (It is
+ technically possible for two invalid normal forms to be isomorphic,
+ but to be considered equivalent, the two instances must also be
+ valid.)
+As with validity, the algorithm suggested by this specification is
+ just one of many possible ways to implement equivalence checking; it
+ is not required that implementations compute normal forms
+ explicitly, only that their determinations of equivalence match
+ those obtained by the algorithm in this specification.
+ </p>
+
+<p><span class="insert">Equivalence is only explicitly specified for
+valid instances (whose normal forms exist and are unique up to
+isomorphism). Implementations may test equivalences involving valid
+and invalid documents. This specification does not constrain the
+behavior of equivalence checking involving invalid instances, provided
+that:
+</span></p>
+<ul>
+ <li><span class="insert">instance equivalence is </span><a href="#dfn-reflexive" class="internalDFN"><span class="insert">reflexive</span></a><span class="insert">, </span><a href="#dfn-symmetric" class="internalDFN"><span class="insert">symmetric</span></a><span class="insert"> and
+ </span><a href="#dfn-transitive" class="internalDFN"><span class="insert">transitive</span></a><span class="insert"> on all instances</span></li>
+ <li><span class="insert"> no valid instance is equivalent to an invalid instance.</span></li>
+ </ul>
+<p><span class="insert">
+Because of the second constraint, equivalence is essentially the union
+ of two equivalence relations on the disjoint sets of valid and
+ invalid instances.
+ There are two simple implementations of equivalence for invalid
+ documents that are correct:</span></p>
+ <ol>
+ <li><span class="insert">each invalid instance is equivalent only to itself</span></li>
+ <li><span class="insert">every pair of invalid instances are equivalent</span></li>
+ </ol>
+
+<h4 id="from-instances-to-bundles-and-documents">From Instances to Bundles and Documents</h4>
+
+<p>PROV documents can contain multiple instances: a <a>toplevel
+instance</a><span class="delete"> consisting of the set of statements not appearing within a bundle,</span><span class="insert">,</span> and
+zero or more<span class="insert"> additional,</span> named instances called <a>bundle</a>s. For the purpose
+of inference and constraint checking, these instances are treated independently. That is,
+a PROV document is valid provided that each instance in it is valid
+and the names of its bundles are distinct. <span class="insert">In other words, there are
+no validity constraints that need to be checked across the different
+instances in a PROV document; the contents of one instance in a
+multi-instance PROV document cannot affect the validity of another instance.
+</span>Similarly, a PROV document is
+equivalent to another if their toplevel instances are equivalent, they
+have the same number of bundles with the same names, and the instances
+of their corresponding bundles are equivalent.<span class="delete"> Analogously to blank nodes</span><span class="insert">
+
+The scope of an existential variable</span> in<span class="delete">
+[</span><span class="delete">RDF</span><span class="delete">], the scope of an existential variable in</span> PROV is<span class="insert"> delimited at</span> the instance
+level, so existential variables with the same name occurring in
+different instances do not necessarily denote the same term. This
+is a consequence of the fact that the instances of two equivalent
+documents only need to be pairwise isomorphic; this is a weaker
+property than requiring that there be a single isomorphism that works
+for all of the corresponding instances.
+</p>
+</section>
+
+<section id="summary-of-inferences-and-constraints">
+<h3><span class="secno">2.5 </span>Summary of inferences and constraints</h3>
+
+<p><a href="">Table 2</a> summarizes the inferences, and
+constraints specified in this document, broken down by component and
+type or relation involved.
+</p>
+
+<span class="delete">Table: work in progress; these entries might change when the document is updated.</span>
+
+
+
+
+
+<div id="prov-constraints-fig" style="text-align: left;">
+<table class="thinborder" style="margin-left: auto; margin-right: auto; border-color: black;">
+<caption id="prov-constraints">Table 2: Summary of inferences and constraints for PROV Types and Relations</caption>
+<tbody><tr><td><a><b>Type or Relation Name</b></a></td><td><b>
+ Inferences and Constraints</b></td><td><b>Component</b></td></tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+
+<tr class="component1-color">
+ <td class="essential"><a>Entity</a></td>
+ <td><a class="rule-text" href="#entity-generation-invalidation-inference_text"><span>Inference 7 (entity-generation-invalidation-inference)</span></a><br>
+ <a class="rule-text" href="#specialization-attributes-inference_text"><span>Inference 21 (specialization-attributes-inference)</span></a><br>
+ <a class="rule-text" href="#key-object_text"><span>Constraint <span class="delete">23</span><span class="insert">22</span> (key-object)</span></a><br>
+ <a class="rule-text" href="#impossible-object-property-overlap_text"><span>Constraint <span class="delete">56</span><span class="insert">54</span> (impossible-object-property-overlap)</span></a><br>
+ <a class="rule-text" href="#entity-activity-disjoint_text"><span>Constraint <span class="delete">57</span><span class="insert">55</span> (entity-activity-disjoint)</span></a><br>
+ </td>
+ <td rowspan="8" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component1" title="Component 1: Entities/Activities">1</a></td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Activity</a></td>
+ <td><a class="rule-text" href="#activity-start-end-inference_text"><span>Inference 8 (activity-start-end-inference)</span></a><br>
+ <a class="rule-text" href="#key-object_text"><span>Constraint <span class="delete">23</span><span class="insert">22</span> (key-object)</span></a><br>
+ <a class="rule-text" href="#unique-startTime_text"><span>Constraint <span class="delete">29</span><span class="insert">28</span> (unique-startTime)</span></a><br>
+ <a class="rule-text" href="#unique-endTime_text"><span>Constraint <span class="delete">30</span><span class="insert">29</span> (unique-endTime)</span></a><br>
+ <a class="rule-text" href="#impossible-object-property-overlap_text"><span>Constraint <span class="delete">56</span><span class="insert">54</span> (impossible-object-property-overlap)</span></a><br>
+ <a class="rule-text" href="#entity-activity-disjoint_text"><span>Constraint <span class="delete">57</span><span class="insert">55</span> (entity-activity-disjoint)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Generation</a></td>
+ <td><a class="rule-text" href="#generation-use-communication-inference_text"><span>Inference 6 (generation-use-communication-inference)</span></a><br>
+
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-generation_text"><span>Constraint <span class="delete">25</span><span class="insert">24</span> (unique-generation)</span></a><br>
+ <a class="rule-text" href="#generation-within-activity_text"><span>Constraint <span class="delete">36</span><span class="insert">34</span> (generation-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-invalidation_text"><span>Constraint <span class="delete">38</span><span class="insert">36</span> (generation-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-usage_text"><span>Constraint <span class="delete">39</span><span class="insert">37</span> (generation-precedes-usage)</span></a><br>
+ <a class="rule-text" href="#generation-generation-ordering_text"><span>Constraint <span class="delete">41</span><span class="insert">39</span> (generation-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#derivation-usage-generation-ordering_text"><span>Constraint <span class="delete">43</span><span class="insert">41</span> (derivation-usage-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#derivation-generation-generation-ordering_text"><span>Constraint <span class="delete">44</span><span class="insert">42</span> (derivation-generation-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasStartedBy-ordering_text"><span>Constraint <span class="delete">45</span><span class="insert">43</span> (wasStartedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasEndedBy-ordering_text"><span>Constraint <span class="delete">46</span><span class="insert">44</span> (wasEndedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#specialization-generation-ordering_text"><span>Constraint <span class="delete">47</span><span class="insert">45</span> (specialization-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint <span class="delete">49</span><span class="insert">47</span> (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAttributedTo-ordering_text"><span>Constraint <span class="delete">50</span><span class="insert">48</span> (wasAttributedTo-ordering)</span></a><br>
+ <a class="rule-text" href="#actedOnBehalfOf-ordering_text"><span>Constraint <span class="delete">51</span><span class="insert">49</span> (actedOnBehalfOf-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Usage</a></td>
+ <td><a class="rule-text" href="#generation-use-communication-inference_text"><span>Inference 6 (generation-use-communication-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#usage-within-activity_text"><span>Constraint <span class="delete">35</span><span class="insert">33</span> (usage-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-usage_text"><span>Constraint <span class="delete">39</span><span class="insert">37</span> (generation-precedes-usage)</span></a><br>
+ <a class="rule-text" href="#usage-precedes-invalidation_text"><span>Constraint <span class="delete">40</span><span class="insert">38</span> (usage-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#derivation-usage-generation-ordering_text"><span>Constraint <span class="delete">43</span><span class="insert">41</span> (derivation-usage-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Communication</a></td>
+ <td><a class="rule-text" href="#communication-generation-use-inference_text"><span>Inference 5 (communication-generation-use-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#wasInformedBy-ordering_text"><span>Constraint <span class="delete">37</span><span class="insert">35</span> (wasInformedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Start</a></td>
+ <td><a class="rule-text" href="#wasStartedBy-inference_text"><span>Inference 9 (wasStartedBy-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-wasStartedBy_text"><span>Constraint <span class="delete">27</span><span class="insert">26</span> (unique-wasStartedBy)</span></a><br>
+ <a class="rule-text" href="#unique-startTime_text"><span>Constraint <span class="delete">29</span><span class="insert">28</span> (unique-startTime)</span></a><br>
+ <a class="rule-text" href="#start-precedes-end_text"><span>Constraint <span class="delete">32</span><span class="insert">30</span> (start-precedes-end)</span></a><br>
+ <a class="rule-text" href="#usage-within-activity_text"><span>Constraint <span class="delete">35</span><span class="insert">33</span> (usage-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-within-activity_text"><span>Constraint <span class="delete">36</span><span class="insert">34</span> (generation-within-activity)</span></a><br>
+ <a class="rule-text" href="#wasInformedBy-ordering_text"><span>Constraint <span class="delete">37</span><span class="insert">35</span> (wasInformedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#start-start-ordering_text"><span>Constraint <span class="delete">33</span><span class="insert">31</span> (start-start-ordering)</span></a><br>
+ <a class="rule-text" href="#wasStartedBy-ordering_text"><span>Constraint <span class="delete">45</span><span class="insert">43</span> (wasStartedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint <span class="delete">49</span><span class="insert">47</span> (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>End</a></td>
+ <td><a class="rule-text" href="#wasEndedBy-inference_text"><span>Inference 10 (wasEndedBy-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-wasEndedBy_text"><span>Constraint <span class="delete">28</span><span class="insert">27</span> (unique-wasEndedBy)</span></a><br>
+ <a class="rule-text" href="#unique-endTime_text"><span>Constraint <span class="delete">30</span><span class="insert">29</span> (unique-endTime)</span></a><br>
+ <a class="rule-text" href="#start-precedes-end_text"><span>Constraint <span class="delete">32</span><span class="insert">30</span> (start-precedes-end)</span></a><br>
+ <a class="rule-text" href="#usage-within-activity_text"><span>Constraint <span class="delete">35</span><span class="insert">33</span> (usage-within-activity)</span></a><br>
+ <a class="rule-text" href="#generation-within-activity_text"><span>Constraint <span class="delete">36</span><span class="insert">34</span> (generation-within-activity)</span></a><br>
+ <a class="rule-text" href="#wasInformedBy-ordering_text"><span>Constraint <span class="delete">37</span><span class="insert">35</span> (wasInformedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#end-end-ordering_text"><span>Constraint <span class="delete">34</span><span class="insert">32</span> (end-end-ordering)</span></a><br>
+ <a class="rule-text" href="#wasEndedBy-ordering_text"><span>Constraint <span class="delete">46</span><span class="insert">44</span> (wasEndedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint <span class="delete">49</span><span class="insert">47</span> (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component1-color">
+ <td class="essential"><a>Invalidation</a></td>
+ <td><a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#unique-invalidation_text"><span>Constraint <span class="delete">26</span><span class="insert">25</span> (unique-invalidation)</span></a><br>
+ <a class="rule-text" href="#generation-precedes-invalidation_text"><span>Constraint <span class="delete">38</span><span class="insert">36</span> (generation-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#usage-precedes-invalidation_text"><span>Constraint <span class="delete">40</span><span class="insert">38</span> (usage-precedes-invalidation)</span></a><br>
+ <a class="rule-text" href="#invalidation-invalidation-ordering_text"><span>Constraint <span class="delete">42</span><span class="insert">40</span> (invalidation-invalidation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasStartedBy-ordering_text"><span>Constraint <span class="delete">45</span><span class="insert">43</span> (wasStartedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#wasEndedBy-ordering_text"><span>Constraint <span class="delete">46</span><span class="insert">44</span> (wasEndedBy-ordering)</span></a><br>
+ <a class="rule-text" href="#specialization-invalidation-ordering_text"><span>Constraint <span class="delete">48</span><span class="insert">46</span> (specialization-invalidation-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint <span class="delete">49</span><span class="insert">47</span> (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#wasAttributedTo-ordering_text"><span>Constraint <span class="delete">50</span><span class="insert">48</span> (wasAttributedTo-ordering)</span></a><br>
+ <a class="rule-text" href="#actedOnBehalfOf-ordering_text"><span>Constraint <span class="delete">51</span><span class="insert">49</span> (actedOnBehalfOf-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+
+<tr class="component2-color">
+ <td class="essential"><a>Derivation</a></td>
+ <td><a class="rule-text" href="#derivation-generation-use-inference_text"><span>Inference 11 (derivation-generation-use-inference)</span></a><br>
+
+
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#derivation-usage-generation-ordering_text"><span>Constraint <span class="delete">43</span><span class="insert">41</span> (derivation-usage-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#derivation-generation-generation-ordering_text"><span>Constraint <span class="delete">44</span><span class="insert">42</span> (derivation-generation-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+ <td rowspan="5" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component2" title="Component 2: Derivations">2</a></td>
+</tr>
+<tr class="component2-color">
+ <td class="provType"><a>Revision</a></td>
+ <td><a class="rule-text" href="#revision-is-alternate-inference_text"><span>Inference 12 (revision-is-alternate-inference)</span></a><br></td>
+</tr>
+<tr class="component2-color">
+ <td class="provType"><a>Quotation</a></td>
+ <td>No specific constraints</td>
+</tr>
+<tr class="component2-color">
+ <td class="provType"><a>Primary Source</a></td>
+ <td>No specific constraints</td>
+</tr>
+<tr class="component2-color">
+ <td><a class="essential">Influence</a></td>
+ <td>No specific constraints</td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component3-color" style="border-collapse: collapse; ">
+ <td class="essential"><a>Agent</a></td>
+ <td><a class="rule-text" href="#key-object_text"><span>Constraint <span class="delete">23</span><span class="insert">22</span> (key-object)</span></a><br>
+ <a class="rule-text" href="#impossible-object-property-overlap_text"><span>Constraint <span class="delete">56</span><span class="insert">54</span> (impossible-object-property-overlap)</span></a><br>
+ </td>
+ <td rowspan="5" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component3" title="Component 3: Agents/Responsibility">3</a></td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Attribution</a></td>
+ <td><a class="rule-text" href="#attribution-inference_text"><span>Inference 13 (attribution-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#wasAttributedTo-ordering_text"><span>Constraint <span class="delete">50</span><span class="insert">48</span> (wasAttributedTo-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Association</a></td>
+ <td><a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#wasAssociatedWith-ordering_text"><span>Constraint <span class="delete">49</span><span class="insert">47</span> (wasAssociatedWith-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Delegation</a></td>
+ <td><a class="rule-text" href="#delegation-inference_text"><span>Inference 14 (delegation-inference)</span></a><br>
+ <a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ <a class="rule-text" href="#actedOnBehalfOf-ordering_text"><span>Constraint <span class="delete">51</span><span class="insert">49</span> (actedOnBehalfOf-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-property-overlap_text"><span>Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+<tr class="component3-color">
+ <td class="essential"><a>Influence</a></td>
+ <td><a class="rule-text" href="#influence-inference_text"><span>Inference 15 (influence-inference)</span></a><br>
+ <a class="rule-text" href="#key-properties_text"><span>Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</span></a><br>
+ </td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component4-color">
+ <td><a title="bundle">Bundle constructor</a></td>
+ <td>No specific constraints; see <a href="#bundle-constraints" class="sectionRef sec-ref">section <span class="delete">6.2</span><span class="insert">7.2</span> Bundles and Documents</a></td>
+ <td rowspan="2" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component4" title="Component 4: Bundles">4</a></td>
+</tr>
+<tr class="component4-color">
+ <td class="provType"><a title="bundle">Bundle type</a></td>
+ <td> No specific constraints; see <a href="#bundle-constraints" class="sectionRef sec-ref">section <span class="delete">6.2</span><span class="insert">7.2</span> Bundles and Documents</a>
+ </td>
+</tr>
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component5-color">
+ <td><a>Alternate</a></td>
+ <td><a class="rule-text" href="#alternate-reflexive_text"><span>Inference 16 (alternate-reflexive)</span></a><br>
+ <a class="rule-text" href="#alternate-transitive_text"><span>Inference 17 (alternate-transitive)</span></a><br>
+ <a class="rule-text" href="#alternate-symmetric_text"><span>Inference 18 (alternate-symmetric)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+ <td rowspan="3" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component5" title="Component 5: Alternate Entities">5</a></td>
+</tr>
+<tr class="component5-color">
+ <td><a>Specialization</a></td>
+ <td><a class="rule-text" href="#specialization-transitive_text"><span>Inference 19 (specialization-transitive)</span></a><br>
+ <a class="rule-text" href="#specialization-alternate-inference_text"><span>Inference 20 (specialization-alternate-inference)</span></a><br>
+ <a class="rule-text" href="#specialization-attributes-inference_text"><span>Inference 21 (specialization-attributes-inference)</span></a><br>
+ <a class="rule-text" href="#specialization-generation-ordering_text"><span>Constraint <span class="delete">47</span><span class="insert">45</span> (specialization-generation-ordering)</span></a><br>
+ <a class="rule-text" href="#specialization-invalidation-ordering_text"><span>Constraint <span class="delete">48</span><span class="insert">46</span> (specialization-invalidation-ordering)</span></a><br>
+ <a class="rule-text" href="#impossible-specialization-reflexive_text"><span>Constraint <span class="delete">54</span><span class="insert">52</span> (impossible-specialization-reflexive)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+
+ <span class="delete">Mention</span>
+ <span class="delete">Inference 22 (mention-specialization-inference)</span>
+ <span class="delete">Constraint 31 (unique-mention)</span>
+ <span class="delete">Constraint 52 (typing)</span>
+
+
+
+
+<tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+
+<tr class="component6-color">
+ <td><a>Collection</a></td>
+ <td> No specific constraints </td>
+ <td rowspan="2" style="text-align: center; "><a href="http://www.w3.org/TR/prov-dm/#component6" title="Component 6: Collections">6</a></td>
+</tr>
+<tr class="component6-color">
+ <td><a>Membership</a></td>
+ <td> <a class="rule-text" href="#membership-empty-collection_text"><span>Constraint <span class="delete">58</span><span class="insert">56</span> (membership-empty-collection)</span></a><br>
+ <a class="rule-text" href="#typing_text"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a><br>
+ </td>
+</tr>
+</tbody></table>
+</div>
+
+
+</section>
+
+</section>
+
+<section id="compliance">
+<h2><span class="secno">3. </span>Compliance with this document</h2>
+
+<p>
+ For the purpose of compliance, the normative sections of this document
+ are <a href="#compliance" class="sectionRef sec-ref">section 3. Compliance with this document</a>,
+<a href="#concepts" class="sectionRef sec-ref">section 4. <span class="insert">Basic concepts</span></a><span class="insert">,
+</span><a href="#inferences" class="sectionRef sec-ref"><span class="insert">section 5. </span>Definitions and Inferences</a>,
+<a href="#constraints" class="sectionRef sec-ref">section <span class="delete">5.</span><span class="insert">6.</span> Constraints</a>, and
+<a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section <span class="delete">6.</span><span class="insert">7.</span> Normalization, Validity, and Equivalence</a>.
+
+
+ To be compliant:
+ </p><ol><li>When processing provenance, an
+ application <em class="rfc2119" title="may">may</em> apply the inferences and definitions in <a href="#inferences" class="sectionRef sec-ref">section <span class="delete">4.</span><span class="insert">5.</span> Definitions and Inferences</a>.</li>
+ <li>If determining whether a PROV instance or document is <a href="#dfn-valid" class="internalDFN">valid</a>, an
+ application <em class="rfc2119" title="must">must</em> <span class="delete">check that</span><span class="insert">determine whether</span> all of the
+ constraints of <a href="#constraints" class="sectionRef sec-ref">section <span class="delete">5.</span><span class="insert">6.</span> Constraints</a> are
+ satisfied on
+ the <a href="#dfn-normal-form" class="internalDFN">normal form</a> of the instance or document. </li>
+ <li> If producing provenance meant for other applications to
+ use, the application <em class="rfc2119" title="should">should</em> produce <a href="#dfn-valid" class="internalDFN">valid</a> provenance, as specified in <a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section <span class="delete">6.</span><span class="insert">7.</span> Normalization, Validity, and Equivalence</a>. </li>
+ <li>If determining whether two PROV instances or documents are
+ <a href="#dfn-equivalent" class="internalDFN">equivalent</a>, an application <em class="rfc2119" title="must">must</em> determine whether their
+ normal forms are equal, as specified in <a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section <span class="delete">6.</span><span class="insert">7.</span> Normalization, Validity, and Equivalence</a>.
+ </li></ol>
+
+ <p><span class="delete">Compliant </span><span class="insert">This specification defines validity and equivalence procedurally
+ via reduction to normal forms. If checking validity or equivalence, the
+ results </span><em class="rfc2119" title="must"><span class="insert">must</span></em><span class="insert"> be the same as would be obtained by computing normal
+ forms as defined in this specification. Applications that explicitly compute
+ normal forms, following the implementation strategy suggested by
+ this specification, are by definition compliant. However,
+ </span>applications <span class="delete">are not required to</span><span class="insert">can also comply by checking validity and equivalence in any
+ other way that yields the same answers without</span> explicitly <span class="delete">compute
+ </span><span class="insert">applying
+ definitions, inferences, and constraints or constructing </span>normal <span class="delete">forms; however, if checking validity or equivalence, the
+ results should be the same as would be obtained by computing normal
+ forms as defined in this specification.</span><span class="insert">forms.</span></p>
+
+ <p>
+ All figures are for illustration purposes
+ only. Information in tables is normative if it appears in a
+ normative section; specifically, <a href="#expandable-parameters-fig">Table 3</a> is normative. Text in appendices and
+in boxes labeled "Remark" is informative. Where there is any apparent
+ ambiguity between the descriptive text and the formal text in a
+ "definition", "inference" or "constraint" box, the formal text takes
+priority.
+ </p>
+
+
+
+
+
+
+
+
+</section>
+
+ <section id="concepts">
+ <h2><span class="secno">4. </span><span class="insert">Basic concepts</span></h2>
+
+ <p><span class="insert">This section specifies the key concepts of terms, statements, instances, substitution,
+ satisfaction, and unification, which have already been discussed in
+ </span><a href="#rationale"><span class="insert">Section 2</span></a><span class="insert">.
+ </span></p>
+
+ <p><span class="insert">Many PROV relation statements have an identifier, identifying a
+ link between two or more related objects. Identifiers can sometimes
+ be omitted in [</span><cite><a class="bibref" href="#bib-PROV-N"><span class="insert">PROV-N</span></a></cite><span class="insert">] notation. For the purpose of inference and
+ validity checking, we generate special identifiers called
+ </span><dfn id="dfn-variables"><span class="insert">variables</span></dfn><span class="insert"> denoting the unknown values.
+ Generally, identifiers occurring in constraints and inferences are
+ variables. Variables that are generated during inferences and
+ appear inside an instance are often called </span><dfn id="dfn-existential-variables"><span class="insert">existential
+ variables</span></dfn><span class="insert">, because they are implicitly existentially quantified.
+</span></p>
+
+ <p><span class="insert"> A </span><dfn id="term"><span class="insert">PROV term</span></dfn><span class="insert"> is a constant identifier
+ </span><span class="math"><span class="insert">c</span></span><span class="insert">, a placeholder </span><span class="name"><span class="insert">-</span></span><span class="insert">, a literal value,
+ or an existential variable </span><span class="math"><span class="insert">x</span></span><span class="insert">. An
+ arbitrary PROV term is written </span><span class="math"><span class="insert">t</span></span><span class="insert">.</span></p>
+
+ <p><span class="insert"> A </span><dfn id="statement"><span class="insert">PROV statement</span></dfn><span class="insert"> is an expression of
+ the form </span><span class="math"><span class="insert">p(t</span><sub><span class="insert">1</span></sub><span class="insert">,...,t</span><sub><span class="insert">n</span></sub><span class="insert">)</span></span><span class="insert"> or </span><span class="math"><span class="insert">p(id;t</span><sub><span class="insert">1</span></sub><span class="insert">,...,t</span><sub><span class="insert">n</span></sub><span class="insert">)</span></span><span class="insert"> where
+ </span><span class="math"><span class="insert">id,t</span><sub><span class="insert">1</span></sub><span class="insert">,...,t</span><sub><span class="insert">n</span></sub></span><span class="insert"> are
+ PROV </span><a><span class="insert">term</span></a><span class="insert">s and </span><span class="math"><span class="insert">p</span></span><span class="insert"> is one of the
+ basic PROV relations. An arbitrary PROV statement is written </span><span class="math"><span class="insert">A</span></span><span class="insert">.</span></p>
+
+<p><span class="insert"> A </span><dfn id="instance"><span class="insert">PROV instance</span></dfn><span class="insert"> is a set of PROV
+ statements. Two instances are considered to be the same if they
+ contain the same statements, without regard to order or repetition.
+ An arbitrary PROV instance is written </span><span class="math"><span class="insert">I</span></span><span class="insert">.
+</span></p>
+
+ <p><span class="insert">A </span><dfn id="substitution"><span class="insert">substitution</span></dfn> <span class="math"><span class="insert">S</span></span><span class="insert"> is a mapping </span><span class="math"><span class="insert">
+ [x</span><sub><span class="insert">1</span></sub><span class="insert">=t</span><sub><span class="insert">1</span></sub><span class="insert">,...,x</span><sub><span class="insert">n</span></sub><span class="insert">=t</span><sub><span class="insert">n</span></sub><span class="insert">]</span></span><span class="insert"> associating existential variables
+ with terms. A substitution is </span><em><span class="insert">applied</span></em><span class="insert"> to a term, statement
+ or instance by replacing all occurrences of each of the variables
+ </span><span class="math"><span class="insert">x</span><sub><span class="insert">i</span></sub></span><span class="insert"> with the corresponding </span><span class="math"><span class="insert">t</span><sub><span class="insert">i</span></sub></span><span class="insert">. Specifically, if </span><span class="math"><span class="insert">S =
+ [x</span><sub><span class="insert">1</span></sub><span class="insert">=t</span><sub><span class="insert">1</span></sub><span class="insert">,...,x</span><sub><span class="insert">n</span></sub><span class="insert">=t</span><sub><span class="insert">n</span></sub><span class="insert">]</span></span><span class="insert">
+ then the application of </span><span class="math"><span class="insert">S</span></span><span class="insert"> to a term, statement or instance, written </span><span class="math"><span class="insert">S(t)</span></span><span class="insert">, </span><span class="math"><span class="insert">S(A)</span></span><span class="insert"> and
+ </span><span class="math"><span class="insert">S(I)</span></span><span class="insert"> respectively, is defined as follows:</span></p>
+<ul><li><span class="math"><span class="insert">S(c) = c</span></span><span class="insert"> if </span><span class="math"><span class="insert">c</span></span><span class="insert"> is a constant identifier.</span></li>
+<li><span class="math"><span class="insert">S(x</span><sub><span class="insert">i</span></sub><span class="insert">) = t</span><sub><span class="insert">i</span></sub></span><span class="insert"> if </span><span class="math"><span class="insert">x</span><sub><span class="insert">i</span></sub></span><span class="insert"> is one of the variables bound to a
+ term </span><span class="math"><span class="insert">t</span><sub><span class="insert">i</span></sub></span><span class="insert"> in </span><span class="math"><span class="insert">S</span></span><span class="insert">.</span></li>
+<li><span class="math"><span class="insert">S(x) = x</span></span><span class="insert"> if </span><span class="math"><span class="insert">x</span></span><span class="insert"> is a variable not bound in </span><span class="math"><span class="insert">S</span></span><span class="insert">.</span></li>
+<li><span class="math"><span class="insert">S(p(t</span><sub><span class="insert">1</span></sub><span class="insert">,...,t</span><sub><span class="insert">n</span></sub><span class="insert">)) = p(S(t</span><sub><span class="insert">1</span></sub><span class="insert">),...,S(t</span><sub><span class="insert">n</span></sub><span class="insert">))</span></span><span class="insert">.</span></li>
+<li><span class="math"><span class="insert">S(p(id;t</span><sub><span class="insert">1</span></sub><span class="insert">,...,t</span><sub><span class="insert">n</span></sub><span class="insert">)) = p(S(id);S(t</span><sub><span class="insert">1</span></sub><span class="insert">),...,S(t</span><sub><span class="insert">n</span></sub><span class="insert">))</span></span><span class="insert">.</span></li>
+<li><span class="math"><span class="insert">S(I) = { S(A) | A ∈ I } </span></span><span class="insert"> if </span><span class="math"><span class="insert">I</span></span><span class="insert"> is an instance.</span></li>
+</ul>
+
+ <p><span class="insert">Suppose </span><span class="math"><span class="insert">A</span></span><span class="insert"> is a statement and </span><span class="math"><span class="insert">I</span></span><span class="insert"> is an
+ instance and </span><span class="math"><span class="insert">S</span></span><span class="insert"> a substitution. We say that </span><span class="math"><span class="insert">A</span></span><span class="insert"> is
+ </span><dfn id="dfn-satisfied"><span class="insert">satisfied</span></dfn><span class="insert"> in </span><span class="math"><span class="insert">I</span></span><span class="insert"> by </span><span class="math"><span class="insert">S</span></span><span class="insert"> if </span><span class="math"><span class="insert">S(A) ∈ I</span></span><span class="insert">. Likewise,
+ we say that a set of statements </span><span class="math"><span class="insert">{A</span><sub><span class="insert">1</span></sub><span class="insert">,...,A</span><sub><span class="insert">n</span></sub><span class="insert">}</span></span><span class="insert"> is satisfied in
+ </span><span class="math"><span class="insert">I</span></span><span class="insert"> if each </span><span class="math"><span class="insert">A</span><sub><span class="insert">i</span></sub></span><span class="insert"> is satisfied in </span><span class="math"><span class="insert">I</span></span><span class="insert"> by </span><span class="math"><span class="insert">S</span></span><span class="insert">. Finally, we
+ say that a set of statements is </span><dfn id="dfn-satisfiable"><span class="insert">satisfiable</span></dfn><span class="insert">
+ in </span><span class="math"><span class="insert">I</span></span><span class="insert"> if there is some substitution </span><span class="math"><span class="insert">S</span></span><span class="insert"> that satisfies the
+ statements in </span><span class="math"><span class="insert">I</span></span><span class="insert">.
+</span></p>
+
+ <p> <dfn id="dfn-unification"><span class="insert">Unification</span></dfn><span class="insert"> is an operation that can be applied
+ to a pair of terms.
+ The result of unification is either a </span><dfn id="dfn-unifier"><span class="insert">unifier</span></dfn><span class="insert">, that is, a substitution </span><span class="math"><span class="insert">S</span></span><span class="insert"> such that </span><span class="math"><span class="insert">S(t)
+ = S(t')</span></span><span class="insert">, or failure, indicating
+ that there is no </span><a href="#dfn-unifier" class="internalDFN"><span class="insert">unifier</span></a><span class="insert">. Unification of pairs of terms is defined as follows.</span></p>
+
+ <ul>
+ <li><span class="insert"> If </span><span class="math"><span class="insert">t</span></span><span class="insert"> and </span><span class="math"><span class="insert">t'</span></span><span class="insert"> are constant identifiers or literal values
+ (including the placeholder </span><span class="name"><span class="insert">-</span></span><span class="insert">), then
+ there are two cases. If </span><span class="math"><span class="insert">t = t'</span></span><span class="insert"> then their </span><a href="#dfn-unifier" class="internalDFN"><span class="insert">unifier</span></a><span class="insert"> is the
+ empty substitution, otherwise unification
+fails. </span></li>
+ <li><span class="insert"> If </span><span class="math"><span class="insert">x</span></span><span class="insert"> is an existential variable
+ and
+ </span><span class="math"><span class="insert">t'</span></span><span class="insert"> is any term (identifier, constant,
+ placeholder </span><span class="name"><span class="insert">-</span></span><span class="insert">, or
+ existential variable), then their
+ </span><a href="#dfn-unifier" class="internalDFN"><span class="insert">unifier</span></a><span class="insert"> is
+ </span><span class="math"><span class="insert">[x=t']</span></span><span class="insert">. In the special case where
+ </span><span class="math"><span class="insert">t'=x</span></span><span class="insert">, the </span><a href="#dfn-unifier" class="internalDFN"><span class="insert">unifier</span></a><span class="insert"> is the empty substitution.</span></li>
+ <li><span class="insert"> If </span><span class="math"><span class="insert">t</span></span><span class="insert"> is any term (identifier, constant,
+ placeholder </span><span class="name"><span class="insert">-</span></span><span class="insert">, or
+ existential variable) and
+ </span><span class="math"><span class="insert">x'</span></span><span class="insert"> is an existential variable, then their
+ </span><a href="#dfn-unifier" class="internalDFN"><span class="insert">unifier</span></a><span class="insert"> is the same as the </span><a href="#dfn-unifier" class="internalDFN"><span class="insert">unifier</span></a><span class="insert"> of </span><span class="math"><span class="insert">x</span></span><span class="insert">
+ and </span><span class="math"><span class="insert">t</span></span><span class="insert">.</span></li>
+ </ul>
+
+
+
+<div class="remark"><span class="insert">Unification is analogous to unification in
+ logic programming and theorem proving, restricted to flat terms with
+constants and variables but no function symbols. No "occurs check" is needed because there are no
+ function symbols.</span></div>
+
+ <p><span class="insert">Two PROV instances </span><span class="math"><span class="insert">I</span></span><span class="insert"> and </span><span class="math"><span class="insert">I'</span></span><span class="insert"> are </span><dfn id="dfn-isomorphic"><span class="insert">isomorphic</span></dfn><span class="insert"> if
+ there exists an invertible substitution </span><span class="math"><span class="insert">S</span></span><span class="insert"> that maps each
+ variable of </span><span class="math"><span class="insert">I</span></span><span class="insert"> to a distinct variable of </span><span class="math"><span class="insert">I'</span></span><span class="insert"> and such that
+ </span><span class="math"><span class="insert">S(I) = I'</span></span><span class="insert">.</span></p>
+
+
+</section>
+<section id="inferences">
+<h2><span class="secno"><span class="insert">5. </span></span>Definitions and Inferences</h2>
+<p>
+This section describes <a title="definition" href="#definition" class="internalDFN">definitions</a> and <a title="inference" href="#inference" class="internalDFN">inferences</a> that <em class="rfc2119" title="may">may</em> be used on
+ provenance data, and <span class="insert">that </span>preserve <a>equivalence</a> on <a href="#dfn-valid" class="internalDFN">valid</a>
+PROV instances (as detailed in <a href="#normalization-validity-equivalence" class="sectionRef sec-ref">section <span class="delete">6.</span><span class="insert">7.</span> Normalization, Validity, and Equivalence</a>).
+A <dfn id="definition">definition</dfn> is a rule that can be applied to
+ PROV instances to replace defined <span class="delete">expressions</span><span class="insert">statements</span> with <span class="delete">definitions.</span><span class="insert">other statements.</span> An <dfn id="inference">inference</dfn> is a rule that can be applied
+ to PROV instances to add new PROV statements. A definition states that a
+ provenance statement is equivalent to some other statements, whereas
+ an inference only states one direction of an <span class="delete">implication; thus,
+ defined provenance statements can be replaced by their definitions.</span><span class="insert">implication.</span>
+</p>
+
+
+<p> Definitions have the following general form:</p>
+
+<div class="definition-example" id="definition-example"><div class="ruleTitle"><a class="internalDFN" href="#definition-example">Definition-example NNN (definition-example)</a></div>
+<p>
+ <span class="name">defined_stmt</span> <span class="conditional">IF AND ONLY IF</span>
+ there exists <span class="name">a<sub>1</sub></span>,..., <span class="name">a<sub>m</sub></span> such that <span class="name">defining_stmt<sub>1</sub></span> and ... and <span class="name">defining_stmt<sub>n</sub></span>.</p>
+ </div>
+
+ <p>
+ A definition can be applied to a PROV instance, since its <span class="name">defined_stmt</span> is defined in
+ terms of other statements. Applying a
+ definition to an instance means that if an occurrence of a defined
+ provenance statement <span class="name">defined_stmt</span>
+ can be found in a PROV instance, then we can remove it and add all of the statements
+<span class="name">defining_stmt<sub>1</sub></span> ... <span class="name">defining_stmt<sub>n</sub></span> to the instance, possibly after generating fresh
+ identifiers <span class="name">a<sub>1</sub></span>,...,<span class="name">a<sub>m</sub></span> for existential variables. In
+ other words, it is safe to replace
+ a defined statement with
+ its definition.
+</p>
+
+
+
+
+ <div class="remark"><span class="insert">
+ We use definitions primarily to expand the compact, concrete
+ PROV-N syntax, including short forms and optional parameters, to the abstract syntax
+ implicitly used in PROV-DM.
+ </span></div>
+
+ <p> Inferences have the following general form:</p>
+<div class="inference-example" id="inference-example"><div class="ruleTitle"><a class="internalDFN" href="#inference-example">Inference-example NNN (inference-example)</a></div>
+<p>
+ <span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and
+<span class="name">hyp<sub>k</sub></span> <span class="conditional">THEN</span>
+ there exists <span class="name">a<sub>1</sub></span> and ... and <span class="name">a<sub>m</sub></span> such that <span class="name">concl<sub>1</sub></span> and ... and <span class="name">concl<sub>n</sub></span>.</p>
+ </div>
+
+<p> Inferences can be applied to PROV instances. Applying an inference to an instance means that if all of the provenance statements matching
+ <span class="name">hyp<sub>1</sub></span>... <span class="name">hyp<sub>k</sub></span>
+ can be found in the instance, then we check whether the conclusion
+ <span class="name">concl<sub>1</sub></span> ... <span class="name">concl<sub>n</sub></span> is <a href="#dfn-satisfied" class="internalDFN">satisfied</a> for some values
+ of existential variables. If so, application of the inference has
+ no effect on the instance. If not, then a copy the
+ conclusion should be added to the instance, after
+ generating fresh identifiers <span class="name">a<sub>1</sub></span>,...,<span class="name">a<sub>m</sub></span> for the existential variables. These fresh
+ identifiers might later be found to be equal to known identifiers;
+ they play a similar role in PROV constraints to existential
+ variables in <span class="delete">logic, to "labeled nulls" in database theory
+ </span><span class="insert">logic </span>[<cite><span class="delete">DBCONSTRAINTS</span><a class="bibref" href="#bib-Logic"><span class="insert">Logic</span></a></cite><span class="delete">], </span><span class="insert">] </span>or <span class="delete">to blank nodes in </span><span class="insert">database theory
+ </span>[<cite><span class="delete">RDF</span><a class="bibref" href="#bib-DBCONSTRAINTS"><span class="insert">DBCONSTRAINTS</span></a></cite><span class="insert">].
+
+ In general, omitted optional parameters to
+ [</span><cite><a class="bibref" href="#bib-PROV-N"><span class="insert">PROV-N</span></a></cite><span class="insert">] statements, or explicit </span><span class="name"><span class="insert">-</span></span><span class="insert">
+ markers, are placeholders for existentially quantified variables;
+ that is, they denote unknown values. There are a few exceptions to
+ this general rule, which are specified in </span><a class="rule-ref" href="#optional-placeholders"><span><span class="insert">Definition 4 (optional-placeholders)</span></span></a><span class="insert">.</span></p>
+
+<p><span class="insert"> Definitions and inferences can be viewed as logical formulas;
+ similar formalisms are often used in rule-based reasoning [</span><cite><a class="bibref" href="#bib-CHR"><span class="insert">CHR</span></a></cite><span class="insert">]
+ and in databases [</span><cite><a class="bibref" href="#bib-DBCONSTRAINTS"><span class="insert">DBCONSTRAINTS</span></a></cite>]. In <span class="delete">general, omitted optional parameters to
+ [</span><span class="delete">PROV-N</span><span class="delete">] statements, or explicit </span><span class="delete">-</span><span class="delete">
+ markers, are placeholders for existentially quantified variables;
+ that is, they denote unknown values. There are a few exceptions to
+ this general rule, which are specified in </span><span class="delete">Definition 4 (optional-placeholders)</span><span class="delete">.</span>
+
+<span class="delete"> Definitions and inferences can be viewed as logical formulas;
+ similar formalisms are often used in rule-based reasoning [</span><span class="delete">CHR</span><span class="delete">]
+ and in databases [</span><span class="delete">DBCONSTRAINTS</span><span class="delete">]. In </span>particular, the identifiers
+ <span class="name">a<sub>1</sub></span> ... <span class="name">a<sub>n</sub></span>
+ should be viewed as existentially quantified variables, meaning that
+ through subsequent reasoning steps they may turn out to be equal to
+ other identifiers that are already known, or to other existentially
+ quantified variables.<span class="delete"> Their treatment is analogous to that of blank
+ nodes in RDF. </span>
+
+ In contrast, distinct URIs or literal values in PROV
+ are assumed to be distinct for the purpose of checking validity or
+ inferences. This issue is discussed in more detail under <a href="#uniqueness-constraints">Uniqueness Constraints</a>.
+ </p>
+
+<p>In a <span class="delete">[definition|inference],</span><span class="insert">definition or inference,</span> term symbols such as <span class="name">id</span>,
+ <span class="name">start</span>, <span class="name">end</span>, <span class="name">e</span>,
+ <span class="name">a</span>, <span class="name">attrs</span>,
+ are assumed to be variables unless otherwise specified. These variables are scoped at
+ the <span class="delete">[definition|inference|constraint]</span><span class="insert">definition, inference, or constraint</span> level, so the rule is equivalent to any one-for-one
+ renaming of the variable names. When several rules are
+ collected within a <span class="delete">[definition|inference]</span><span class="insert">definition or inference</span>
+ as an ordered list, the scope of the variables in each rule is at the level of list elements, and so reuse of
+ variable names in different rules does not affect the meaning.
+</p>
+<section id="optional-identifiers-and-attributes">
+ <h3><span class="secno"><span class="delete">4.1</span><span class="insert">5.1</span> </span>Optional Identifiers and Attributes</h3>
+
+ <span class="delete">Many PROV relation statements have an identifier, identifying a
+ link between two or more related objects. Identifiers can sometimes
+ be omitted in [</span><span class="delete">PROV-O</span><span class="delete">] notation. For the purpose of inference and
+ validity checking, we generate special identifiers called
+ </span><span class="delete">existential variables</span><span class="delete"> denoting the unknown values.
+</span>
+<span class="delete">
+Existential variables can be </span><span class="delete">substituted</span><span class="delete">
+ with other terms. Specifically, a
+ </span><span class="delete">substitution</span><span class="delete"> is a function from a set of existential
+ variables to identifiers, literals, the placeholder </span><span class="delete">-</span><span class="delete">,
+ or other </span><span class="delete">existential variables</span><span class="delete">. A substitution </span><span class="delete">S</span><span class="delete"> can be
+ applied to an instance </span><span class="delete">I</span><span class="delete"> by replacing all occurrences of existential
+ variables </span><span class="delete">x</span><span class="delete"> in the instance with </span><span class="delete">S(x)</span><span class="delete">.
+</span>
+
+
+
+
+
+
+<p>
+<a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a>,
+<a class="rule-ref" href="#optional-attributes"><span>Definition 2 (optional-attributes)</span></a>, and
+<a class="rule-ref" href="#definition-short-forms"><span>Definition 3 (definition-short-forms)</span></a>,
+ explain how to expand the compact forms of PROV-N notation into a
+ normal form. <a class="rule-ref" href="#optional-placeholders"><span>Definition 4 (optional-placeholders)</span></a> indicates when
+ other optional parameters can be replaced by <a href="#dfn-existential-variables" class="internalDFN">existential
+ variables</a>.
+</p>
+
+ <div class="definition" id="optional-identifiers"><div class="ruleTitle"><a class="internalDFN" href="#optional-identifiers">Definition 1 (optional-identifiers)</a></div>
+<p>For each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+<span class="name">wasInfluencedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasDerivedFrom</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>}, the following
+ definitional rules hold:</p>
+ <ol> <li>
+ <span class="name">r(a<sub>1</sub>,...,a<sub>n</sub>) </span> <span class="conditional">IF AND ONLY IF</span>
+ there exists <span class="name">id</span> such that <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>)</span>.</li>
+ <li> <span class="name">r(-; a<sub>1</sub>,...,a<sub>n</sub>) </span> <span class="conditional">IF AND ONLY IF</span>
+ there exists <span class="name">id</span> such that <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>)</span>.</li>
+ </ol>
+ </div>
+
+ <p>Likewise, many PROV-N statements allow for an optional attribute
+ list. If it is omitted, this is the same as specifying an empty
+ attribute list:</p>
+ <div class="definition" id="optional-attributes"><div class="ruleTitle"><a class="internalDFN" href="#optional-attributes">Definition 2 (optional-attributes)</a></div>
+<ol>
+ <li>
+ For each <span class="name">p</span> in {<span class="name">entity</span>, <span class="name">activity</span>,
+ <span class="name">agent</span>}, if <span class="name">a<sub>n</sub></span> is not an attribute
+ list parameter then the following definitional rule holds:
+ <p><span class="name">p(a<sub>1</sub>,...,a<sub>n</sub>)</span>
+ <span class="conditional">IF AND ONLY IF</span> <span class="name">p(a<sub>1</sub>,...,a<sub>n</sub>,[])</span>.
+ </p></li>
+ <li>
+ For each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidated</span>,
+<span class="name">wasInfluencedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasDerivedFrom</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>}, if <span class="name">a<sub>n</sub></span> is not an
+ attribute list parameter then the following definition holds:
+
+ <p> <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>)</span>
+ <span class="conditional">IF AND ONLY IF</span> <span class="name">r(id; a<sub>1</sub>,...,a<sub>n</sub>,[])</span>.</p></li></ol>
+ </div>
+
+
+ <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>.
+do not apply to <span class="name">alternateOf</span><span class="delete">,</span><span class="insert"> and</span> <span class="name">specializationOf<span class="delete">, and </span><span class="delete">mentionOf</span></span>, which do not have identifiers and attributes.
+</p>
+ </div>
+
+
+ <p> Finally, many PROV
+ statements have other optional arguments or short forms that can be
+ used if none of the optional arguments is present. These are
+ handled by specific rules listed below. </p>
+
+<div class="definition" id="definition-short-forms"><div class="ruleTitle"><a class="internalDFN" href="#definition-short-forms">Definition 3 (definition-short-forms)</a></div>
+ <p>
+
+ </p><ol>
+ <li> <span class="name">activity(id,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">activity(id,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasGeneratedBy(id; e,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasGeneratedBy(id; e,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">used(id; a,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">used(id; a,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasStartedBy(id; a,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasStartedBy(id; a,-,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasEndedBy(id; a,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasEndedBy(id; a,-,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasInvalidatedBy(id; e,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasInvalidatedBy(id; e,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasDerivedFrom(id; e2,e1,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasDerivedFrom(id; e2,e1,-,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">wasAssociatedWith(id; e,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">wasAssociatedWith(id; e,-,-,attrs)</span>.
+ </li>
+ <li><span class="name">actedOnBehalfOf(id; a2,a1,attrs)</span> <span class="conditional">IF AND ONLY IF</span> <span class="name">actedOnBehalfOf(id; a2,a1,-,attrs)</span>.
+ </li>
+ </ol>
+ </div>
+
+ <div class="remark">
+
+
+ <p>
+There are no expansion rules for entity, agent, communication,
+ attribution, influence, alternate, <span class="delete">specialization, </span>or <span class="delete">mention
+ </span><span class="insert">specialization
+ </span>relations, because these
+ have no optional parameters aside from the identifier and attributes,
+ which are expanded by the rules in <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>
+ </div>
+
+
+<p id="optional-placeholders_text">Finally, most optional parameters (written <span class="name">-</span>) are, for the purpose of this document,
+ considered to be distinct, fresh existential variables. Optional parameters are defined in [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] and in [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>] for each type of PROV statement.
+ Thus,
+ before proceeding to apply other definitions or inferences, most
+ occurrences of <span class="name">-</span> are to be replaced
+ by fresh existential variables, distinct from any others occurring in
+ the instance.
+ The only exceptions to this general rule, where <span class="name">-</span> are to be left
+ in place, are the <a href="http://www.w3.org/TR/prov-dm/#derivation.activity">activity</a>, <a href="http://www.w3.org/TR/prov-dm/#derivation.generation">generation</a>, and <a href="http://www.w3.org/TR/prov-dm/#derivation.usage">usage</a> parameters in <span class="name">wasDerivedFrom</span> and
+ the <a href="http://www.w3.org/TR/prov-dm/#association.plan">plan</a>
+ parameter in <span class="name">wasAssociatedWith</span>. This is
+ further explained in remarks below.
+ </p>
+
+ <p>The treatment of optional parameters is specified formally using
+ the auxiliary concept of <dfn id="dfn-expandable-parameter">expandable parameter</dfn>. An
+ expandable parameter is one that can be omitted using the
+ placeholder <span class="name">-</span>, and if so, it is
+ to be replaced by a fresh existential identifier.
+ <a href="#expandable-parameters-fig">Table 3</a> defines the <a href="#dfn-expandable-parameter" class="internalDFN">expandable
+ parameter</a>s of the properties of PROV, needed in <a class="rule-ref" href="#optional-placeholders"><span>Definition 4 (optional-placeholders)</span></a>. For emphasis, the four optional parameters
+ that are not <a title="expandable parameter" href="#dfn-expandable-parameter" class="internalDFN">expandable</a> are
+ also listed. Parameters that cannot have value <span class="name">-</span>, and identifiers that are
+ expanded by <a class="rule-ref" href="#optional-identifiers"><span>Definition 1 (optional-identifiers)</span></a>, are not listed.</p>
+ <div id="expandable-parameters-fig">
+ <table id="expandable-parameters_table" border="1" class="thinborder" style="margin-left: auto; margin-right: auto; border-color: black;">
+<caption id="expandable-parameters">Table 3: Expandable and
+ Non-Expandable Parameters</caption>
+<tbody><tr><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td><td style="border-width: 0px; "></td></tr>
+ <tr>
+ <th>Relation</th>
+ <th>Expandable </th>
+ <th>Non-expandable</th>
+ </tr>
+ <tr>
+ <td class="name">used(id; a,e,t,attrs)</td>
+ <td class="name">e,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasGeneratedBy(id; e,a,t,attrs)</td>
+ <td class="name">a,t</td>
+ <td></td>
+ </tr>
+
+ <tr>
+ <td class="name">wasStartedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">e,a1,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasEndedBy(id; a2,e,a1,t,attrs)</td>
+ <td class="name">e,a1,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasInvalidatedBy(id; e,a,t,attrs)</td>
+ <td class="name">a,t</td>
+ <td></td>
+ </tr>
+ <tr>
+ <td class="name">wasDerivedFrom(id; e2,e1,-,g,u,attrs)</td>
+ <td class="name"></td>
+ <td class="name">g,u</td>
+ </tr> <tr>
+ <td class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)<br>(where <span class="name">a</span> is not placeholder <span class="name">-</span>)</td>
+ <td class="name">g,u</td>
+ <td class="name">a</td>
+ </tr>
+
+
+
+ <tr>
+ <td class="name">wasAssociatedWith(id; a,ag,pl,attrs)</td>
+ <td class="name">ag</td>
+ <td class="name">pl</td>
+ </tr>
+ <tr>
+ <td class="name">actedOnBehalfOf(id; ag2,ag1,a,attrs)</td>
+ <td class="name">a</td>
+ <td></td>
+ </tr>
+
+ </tbody></table>
+ </div>
+
+<p> <a class="rule-ref" href="#optional-placeholders"><span>Definition 4 (optional-placeholders)</span></a> states how parameters are to be expanded,
+ using the expandable parameters defined in <a href="#expandable-parameters-fig">Table 3</a>. The last two parts, 4 and 5,
+ indicate how to handle expansion of parameters for
+ <span class="name">wasDerivedFrom</span> expansion, which is only allowed for the
+ generation and use parameters when the activity is specified.
+ 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 <span class="delete">acitivity,</span><span class="insert">activity,</span> would therefore not be justified. </p>
+
+
+<p> A later constraint, <a class="rule-ref" href="#impossible-unspecified-derivation-generation-use"><span>Constraint <span class="delete">53</span><span class="insert">51</span> (impossible-unspecified-derivation-generation-use)</span></a>,
+ forbids specifying generation and use parameters when the activity
+ is unspecified.</p>
+
+ <div class="definition" id="optional-placeholders"><div class="ruleTitle"><a class="internalDFN" href="#optional-placeholders">Definition 4 (optional-placeholders)</a></div>
+ <ol><li>
+ <span class="name">activity(id,-,t2,attrs)</span> <span class="conditional">IF AND ONLY
+ IF</span> there exists <span class="name">t1</span> such that <span class="name">activity(id,t1,t2,attrs)</span>. Here, <span class="name">t2</span> <em class="rfc2119" title="may">may</em> be a placeholder.
+ </li>
+<li> <span class="name">activity(id,t1,-,attrs)</span> <span class="conditional">IF AND ONLY
+ IF</span> there exists <span class="name">t2</span> such that <span class="name">activity(id,t1,t2,attrs)</span>. Here, <span class="name">t1</span> <span class="delete">must not</span><em class="rfc2119" title="may"><span class="insert">may</span></em> be a placeholder.
+</li>
+
+ <li>For each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+
+
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>
+
+ }, if the <span class="name">i</span>th parameter
+ of <span class="name">r</span> is an <a href="#dfn-expandable-parameter" class="internalDFN">expandable parameter</a>
+ of <span class="name">r</span>
+ as specified in <a href="#expandable-parameters-fig">Table 3</a>
+then the following definition holds:
+ <p> <span class="name">r(a<sub>0</sub>;...,a<sub>i-1</sub>, -, a<sub>i+1</sub>, ...,a<sub>n</sub>) </span> <span class="conditional">IF AND ONLY IF</span> there exists <span class="name">a'</span>
+ such that <span class="name">r(a<sub>0</sub>;...,a<sub>i-1</sub>,a',a<sub>i+1</sub>,...,a<sub>n</sub>)</span>.
+ </p></li>
+ <li>If <span class="name">a</span> is not the placeholder <span class="name">-</span>, and <span class="name">u</span> is any term, then the following definition holds:
+ <p> <span class="name"><span class="delete">wasDerivedFrom(id;e2,e1,a,-,u,attrs)</span><span class="insert">wasDerivedFrom(id; e2,e1,a,-,u,attrs)</span></span> <span class="conditional">IF AND ONLY IF</span> there exists <span class="name">g</span>
+ such that <span class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)</span>.</p></li>
+ <li>If <span class="name">a</span> is not the placeholder <span class="name">-</span>, and <span class="name">g</span> is any term,
+ then the following definition holds:
+ <p> <span class="name"><span class="delete">wasDerivedFrom(id;e2,e1,a,g,-,attrs)</span><span class="insert">wasDerivedFrom(id; e2,e1,a,g,-,attrs)</span></span> <span class="conditional">IF AND ONLY IF</span> there exists <span class="name">u</span>
+ such that <span class="name">wasDerivedFrom(id; e2,e1,a,g,u,attrs)</span>.</p></li></ol>
+ </div>
+
+ <div class="remark">
+<p>In an association of the form
+ <span class="name">wasAssociatedWith(id; a,ag,-,attr)</span>, the
+ absence of a plan means: either no plan exists, or a plan exists but
+ it is not identified. Thus, it is not equivalent to <span class="name">wasAssociatedWith(id; a,ag,p,attr)</span> where a
+ plan <span class="name">p</span> is given.</p>
+</div>
+ <div class="remark">
+<p> A derivation <span class="name">wasDerivedFrom(id; e2,e1,a,gen,use,attrs)</span> that
+ specifies an activity explicitly indicates that this activity achieved the derivation, with a usage <span class="name">use</span> of entity <span class="name">e1</span>, and a generation <span class="name">gen</span> of entity <span class="name">e2</span>.
+ It differs from a derivation of the form
+ <span class="name">wasDerivedFrom(id; e2,e1,-,-,-,attrs)</span> with
+ missing activity, generation, and usage. In the latter form, it is not specified
+ if one or more activities are involved in the derivation. </p>
+
+ <p>Let us consider a system, in which a derivation is underpinned by multiple activities. Conceptually, one could also model such a system with a new activity that encompasses the two original activities and underpins the derivation. The inferences defined in this specification do not allow the latter modelling to be inferred from the former. Hence, the two modellings of the same system are regarded as different in the context of this specification.</p>
+ </div>
+</section>
+
+<section id="entities-and-activities">
+ <h3><span class="secno"><span class="delete">4.2</span><span class="insert">5.2</span> </span>Entities and Activities</h3>
+
+
+
+
+<p id="communication-generation-use-inference_text">Communication between activities <a title="definition" href="#definition" class="internalDFN">implies</a> the existence of an underlying
+entity generated by one activity and used by the other, and vice versa.</p>
+
+<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>
+<p>
+<span class="conditional">IF</span>
+<span class="name">wasInformedBy(_id; a2,a1,_attrs)</span>
+<span class="conditional">THEN</span>
+ there exist <span class="name">e</span>, <span class="name">_gen</span>, <span class="name">_t1</span>, <span class="name">_use</span>, and <span class="name">_t2</span>,
+such that <span class="name">wasGeneratedBy(_gen; e,a1,_t1,[])</span> and <span class="name">used(_use; a2,e,_t2,[])</span> hold.</p>
+</div>
+
+
+<p id="generation-use-communication-inference_text">
+
+ </p><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>
+<p>
+<span class="conditional">IF</span> <span class="name">wasGeneratedBy(_gen; e,a1,_t1,_attrs1)</span>
+ and <span class="name">used(_id2; a2,e,_t2,_attrs2)</span> hold
+ <span class="conditional">THEN</span>
+ there exists <span class="name">_id</span>
+such that <span class="name">wasInformedBy(_id; a2,a1,[])</span>
+</p></div>
+
+
+ <div class="remark">
+<p>The relationship <span class="name">wasInformedBy</span> is not
+<a href="#dfn-transitive" class="internalDFN">transitive</a>. Indeed, consider the following statements.</p>
+<pre class="codeexample">wasInformedBy(a2,a1)
+wasInformedBy(a3,a2)
+</pre>
+<p> We cannot infer <span class="name">wasInformedBy(a3,a1)</span>
+ from these statements alone. Indeed,
+from
+<span class="name">wasInformedBy(a2,a1)</span>, we know that there exists <span class="name">e1</span> such that <span class="name">e1</span> was generated by <span class="name">a1</span>
+and used by <span class="name">a2</span>. Likewise, from <span class="name">wasInformedBy(a3,a2)</span>, we know that there exists <span class="name">e2</span> such that <span class="name">e2</span> was generated by <span class="name">a2</span>
+and used by <span class="name">a3</span>. The following illustration
+shows a counterexample to transitivity. The
+horizontal axis represents the event line. We see that <span class="name">e1</span> was generated after <span class="name">e2</span> was used. Furthermore, the illustration also shows that
+<span class="name">a3</span> completes before <span class="name">a1</span> started. So in this example (with no other
+ information) it is impossible for <span class="name">a3</span> to have used an entity generated by <span class="name">a1</span>. This is illustrated in <a href="#counterexample-wasInformedBy">Figure 2</a>.</p>
+
+<div style="text-align: center;">
+<span class="figure" id="fig-figure-2-counter-example-for-transitivity-of-wasinformedby">
+<img src="images/constraints/informedByNonTransitive.png" alt="non transitivity of wasInformedBy">
+<br>
+<span class="figcaption" id="counterexample-wasInformedBy">Figure 2<sup><a class="internalDFN" href="#counterexample-wasInformedBy"><span class="diamond"> ◊:</span></a></sup> Counter-example for transitivity of wasInformedBy</span>
+</span>
+</div>
+</div>
+
+
+
+<hr>
+
+
+
+<p id="entity-generation-invalidation-inference_text">
+From an entity statement, we can infer the existence of
+generation and invalidation events.
+</p>
+<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>
+<p>
+<span class="conditional">IF</span> <span class="name">entity(e,_attrs)</span> <span class="conditional">THEN</span> there exist
+<span class="name">_gen</span>, <span class="name">_a1</span>, <span class="name">_t1</span>,
+<span class="name">_inv</span>, <span class="name">_a2</span>, and <span class="name">_t2</span> such that
+ <span class="name">wasGeneratedBy(_gen; e,_a1,_t1,[])</span> and <span class="name">wasInvalidatedBy(_inv; e,_a2,_t2,[])</span>.
+</p></div>
+
+
+<hr>
+
+
+<p id="activity-start-end-inference_text">
+From an activity statement, we can infer
+start and end events whose times match the start and end times of
+the activity, respectively.
+</p>
+<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>
+<p>
+<span class="conditional">IF</span> <span class="name">activity(a,t1,t2,_attrs)</span> <span class="conditional">THEN</span> there exist <span class="name">_start</span>, <span class="name">_e1</span>, <span class="name">_a1</span>, <span class="name">_end</span>, <span class="name">_a2</span>,
+ and <span class="name">_e2</span> such that
+ <span class="name">wasStartedBy(_start; a,_e1,_a1,t1,[])</span> and <span class="name">wasEndedBy(_end; a,_e2,_a2,t2,[])</span>.
+</p></div>
+
+
+<hr>
+
+
+<p id="wasStartedBy-inference_text">The start of an activity <span class="name">a</span> triggered by entity <span class="name">e1</span>
+implies that
+<span class="name">e1</span> was generated by the starting activity <span class="name">a1</span>.</p>
+
+<div class="inference" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div>
+<p><span class="conditional">IF</span>
+ <span class="name">wasStartedBy(_id; a,e1,a1,_t,_attrs)</span>,
+<span class="conditional">THEN</span> there exist <span class="name">_gen</span> and <span class="name">_t1</span>
+such that
+ <span class="name">wasGeneratedBy(_gen; e1,a1,_t1,[])</span>.</p>
+</div>
+<p>
+
+</p><hr>
+
+<p id="wasEndedBy-inference_text">Likewise,
+the ending of activity <span class="name">a</span> by triggering entity <span class="name">e1</span> implies that
+<span class="name">e1</span> was generated by the ending activity <span class="name">a1</span>.
+</p>
+
+<div class="inference" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div>
+<p><span class="conditional">IF</span>
+ <span class="name">wasEndedBy(_id; a,e1,a1,_t,_attrs)</span>,
+<span class="conditional">THEN</span> there exist <span class="name">_gen</span> and <span class="name">_t1</span> such that
+ <span class="name">wasGeneratedBy(_gen; e1,a1,_t1,[])</span>.</p>
+</div>
+
+
+
+
+</section>
+
+ <section id="derivations">
+<h3><span class="secno"><span class="delete">4.3</span><span class="insert">5.3</span> </span>Derivations</h3>
+
+
+<hr>
+<p id="derivation-generation-use-inference_text">Derivations with explicit
+activity, generation, and usage admit the following inference: </p>
+
+<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>
+<p> In this inference, none of <span class="name">a</span>, <span class="name">gen2</span> or <span class="name">use1</span> can be
+ placeholders <span class="name">-</span>.
+ </p><p>
+<span class="conditional">IF</span> <span class="name">wasDerivedFrom(_id; e2,e1,a,gen2,use1,_attrs)</span>,
+ <span class="conditional">THEN</span> there exists <span class="name">_t1</span> and <span class="name">_t2</span> such that <span class="name">used(use1; a,e1,_t1,[])</span> and <span class="name">wasGeneratedBy(gen2; e2,a,_t2,[])</span>.
+</p>
+</div>
+<p>
+
+
+
+
+</p><hr>
+<p id="revision-is-alternate-inference_text">A revision admits the following inference, stating that the two entities
+linked by a revision are also alternates.</p>
+
+<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>
+ <p>In this inference, any of <span class="name">_a</span>, <span class="name">_g</span> or <span class="name">_u</span> <em class="rfc2119" title="may">may</em> be placeholders.</p>
+<p>
+ <span class="conditional">IF</span> <span class="name">wasDerivedFrom(_id; e2,e1,_a,_g,_u,[prov:type='prov:Revision'])</span>, <span class="conditional">THEN</span> <span class="name">alternateOf(e2,e1)</span>.
+</p>
+
+</div>
+
+
+
+
+<div class="remark">
+ There is no inference stating that <span class="name">wasDerivedFrom</span> is
+ transitive.
+ </div>
+</section>
+
+
+<section id="agents">
+<h3><span class="secno"><span class="delete">4.4</span><span class="insert">5.4</span> </span>Agents</h3>
+
+<p id="attribution-inference_text"> Attribution is the ascribing of an entity to an agent. An
+entity can only be ascribed to an agent if the agent was associated with
+an activity that generated the entity. If the activity, generation
+and association events are not explicit in the instance, they can
+be inferred.</p>
+
+<div class="inference" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">wasAttributedTo(_att; e,ag,_attrs)</span>
+
+<span class="conditional">THEN</span> there exist
+ <span class="name">a</span>,
+ <span class="name">_t</span>,
+<span class="name">_gen</span>,
+<span class="name">_assoc</span>,
+ <span class="name">_pl</span>,
+such that
+<span class="name">wasGeneratedBy(_gen; e,a,_t,[])</span> and
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,[])</span>.
+</p>
+</div>
+
+<div class="remark">
+ In the above inference, <span class="name">_pl</span> is an
+ existential variable, so it can be<span class="delete">
+ merged </span><span class="insert"> unified
+</span>with a constant identifier, another existential variable, or a
+ placeholder <span class="name">-</span>, as explained
+ in the definition of <span class="delete">merging</span><a><span class="insert">unification</span></a>.
+ </div>
+<hr>
+<p id="delegation-inference_text"> Delegation relates agents where one agent acts on behalf of
+another, in the context of some activity. The supervising agent
+delegates some responsibility for part of the activity to the
+subordinate agent, while retaining some responsibility for the overall
+activity. Both agents are associated with this activity.</p>
+
+
+<div class="inference" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">actedOnBehalfOf(_id; ag1, ag2, a, _attrs)</span>
+<span class="conditional">THEN</span> there exist <span class="name">_id1</span>, <span class="name">_pl1</span>, <span class="name">_id2</span>, and <span class="name">_pl2</span> such that <span class="name">wasAssociatedWith(_id1; a, ag1, _pl1, [])</span>
+ and <span class="name">wasAssociatedWith(_id2; a, ag2, _pl2,
+ [])</span>.
+</p>
+</div>
+
+
+<div class="remark">
+ The two associations between the agents and the activity
+ may have different identifiers, different plans, and different
+ attributes. In particular, the plans of the two agents need not be
+ the same, and one, both, or neither can be the placeholder <span class="name">-</span>
+ indicating that there is no plan, because the existential variables
+ <span class="name">_pl1</span> and <span class="name">_pl2</span>
+ can be replaced with constant identifiers, existential variables, or
+ placeholders <span class="name">-</span> independently, as explained
+ in the definition of <span class="delete">merging</span><a><span class="insert">unification</span></a>.
+ </div>
+
+<hr>
+<p id="influence-inference_text">
+The <span class="name">wasInfluencedBy</span> relation is implied by other relations, including
+usage, start, end, generation, invalidation, communication,
+derivation, attribution, association, and delegation. To capture this
+explicitly, we allow the following inferences:
+</p>
+<div class="inference" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div>
+<p>
+ </p><ol>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasGeneratedBy(id; e,a,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e, a, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">used(id; a,e,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a, e, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasInformedBy(id; a2,a1,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a2, a1, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasStartedBy(id; a2,e,a1,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a2, e, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasEndedBy(id; a2,e,_a1,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a2, e, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasInvalidatedBy(id; e,a,_t,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e, a, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasDerivedFrom(id; e2, e1, a, g, u, attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e2, e1, attrs)</span>. Here,
+ <span class="name">a</span>, <span class="name">g</span>, <span class="name">u</span> <em class="rfc2119" title="may">may</em> be placeholders <span class="name">-</span>.
+ </li>
+<li>
+ <span class="conditional">IF</span> <span class="name">wasAttributedTo(id; e,ag,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; e, ag, attrs)</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">wasAssociatedWith(id; a,ag,_pl,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; a, ag, attrs)</span>. Here,
+ <span class="name">_pl</span> <em class="rfc2119" title="may">may</em> be a placeholder <span class="name">-</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span> <span class="name">actedOnBehalfOf(id; ag2,ag1,_a,attrs)</span> <span class="conditional">THEN</span> <span class="name">wasInfluencedBy(id; ag2, ag1, attrs)</span>.
+ </li>
+</ol>
+</div>
+
+<div class="remark">
+ The inferences above permit the use of same identifier for an
+ influence relationship and a more
+ specific relationship.
+</div>
+
+</section>
+
+
+
+ <section id="alternate-and-specialized-entities">
+<h3><span class="secno"><span class="delete">4.5</span><span class="insert">5.5</span> </span>Alternate and Specialized Entities</h3>
+
+
+
+
+<hr>
+ <p id="alternate-reflexive_text">The relation <span class="name">alternateOf</span> is an <a href="#dfn-equivalence-relation" class="internalDFN">equivalence relation</a><span class="delete">:</span><span class="insert"> on
+ entities:</span> that is,
+ it is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>,
+ <a href="#dfn-transitive" class="internalDFN">transitive</a> and <a href="#dfn-symmetric" class="internalDFN">symmetric</a>. As a consequence, the
+ following inferences can be applied:</p>
+
+
+<div class="inference" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">entity(e)</span> <span class="conditional">THEN</span>
+<span class="name">alternateOf(e,e)</span>.
+</p>
+ </div>
+
+<p>
+
+</p><hr>
+ <p id="alternate-transitive_text">
+
+ </p><div class="inference" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">alternateOf(e1,e2)</span> and
+ <span class="name">alternateOf(e2,e3)</span> <span class="conditional">THEN</span> <span class="name">alternateOf(e1,e3)</span>.</p>
+ </div>
+
+<p>
+
+</p><hr>
+ <p id="alternate-symmetric_text">
+
+ </p><div class="inference" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">alternateOf(e1,e2)</span> <span class="conditional">THEN</span> <span class="name">alternateOf(e2,e1)</span>.</p>
+ </div>
+
+<p>
+
+
+</p><hr>
+<p id="specialization-transitive_text">
+Similarly, specialization is a
+ <a href="#dfn-strict-partial-order" class="internalDFN">strict partial order</a>: it is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>. Irreflexivity is handled later as <a class="rule-ref" href="#impossible-specialization-reflexive"><span>Constraint <span class="delete">54</span><span class="insert">52</span> (impossible-specialization-reflexive)</span></a>
+ </p>
+ <div class="inference" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div>
+<p>
+
+<span class="conditional">IF</span> <span class="name">specializationOf(e1,e2)</span>
+ and
+ <span class="name">specializationOf(e2,e3)</span> <span class="conditional">THEN</span> <span class="name">specializationOf(e1,e3)</span>.</p>
+ </div>
+
+<p>
+
+</p><hr>
+
+ <p id="specialization-alternate-inference_text">If one entity specializes another, then they are also
+ alternates:</p>
+
+ <div class="inference" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div>
+<p>
+
+<span class="conditional">IF</span> <span class="name">specializationOf(e1,e2)</span> <span class="conditional">THEN</span> <span class="name">alternateOf(e1,e2)</span>.</p>
+ </div>
+
+<hr>
+<p id="specialization-attributes-inference_text">
+ If one entity specializes another then all attributes of the more
+ general entity are also attributes of the more specific one.
+ </p>
+<div class="inference" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div>
+ <p>
+
+<span class="conditional">IF</span> <span class="name">entity(e1, attrs)</span> and <span class="name">specializationOf(e2,e1)</span>, <span class="conditional">THEN </span>
+ <span class="name">entity(e2, attrs)</span>.</p>
+ </div>
+
+
+
+
+
+
+<span class="delete">Note: The following inference is associated with a feature "</span><span class="delete">at risk</span><span class="delete">" and may be removed from this specification based on feedback. Please send feedback to public-prov-comments@w3.org.</span>
+
+
+
+ <span class="delete">If one entity is a mention of another in a bundle, then the former is also a specialization of the latter:</span>
+
+ <span class="delete">Inference 22 (mention-specialization-inference)</span>
+
+<span class="delete">IF</span> <span class="delete">mentionOf(e2,e1,b)</span> <span class="delete">THEN</span> <span class="delete">specializationOf(e2,e1)</span><span class="delete">.</span>
+
+
+
+
+
+
+
+
+</section>
+
+
+
+
+
+</section>
+
+
+
+<section id="constraints">
+<h2><span class="secno"><span class="delete">5.</span><span class="insert">6.</span> </span>Constraints</h2>
+
+
+
+
+<p>
+This section defines a collection of constraints on PROV instances.
+There are three kinds of constraints:
+ </p><ul><li><em>uniqueness constraints</em> that say that a <a href="#instance" class="internalDFN">PROV
+ instance</a> can contain at most one statement of each kind with a
+ given identifier. For
+ example, if we describe the same generation event twice, then the
+ two statements should have the same times;
+ </li>
+ <li> <em>event ordering constraints</em> that say that it
+ should be possible to arrange the
+ events (generation, usage, invalidation, start, end) described in a
+ PROV instance into a <a href="#dfn-preorder" class="internalDFN">preorder</a> that corresponds to a sensible
+ "history" (for example, an entity should not be generated after it
+ is used); and
+ </li>
+ <li><em>impossibility constraints</em>, which forbid certain
+ patterns of statements in <a href="#dfn-valid" class="internalDFN">valid</a> PROV instances.
+ </li></ul>
+
+ <p>As in a <span class="delete">[definition|inference],</span><span class="insert">definition or inference,</span> term symbols such as <span class="name">id</span>,
+ <span class="name">start</span>, <span class="name">end</span>, <span class="name">e</span>,
+ <span class="name">a</span>, <span class="name">attrs</span> in a constraint,
+ are assumed to be variables unless otherwise specified. These variables are scoped at
+ the constraint level, so the rule is equivalent to any one-for-one
+ renaming of the variable names. When several rules are collected within a constraint
+ as an ordered list, the scope of the variables in each rule is at the level of list elements, and so reuse of
+ variable names in different rules does not affect the meaning.
+</p>
+ <section id="uniqueness-constraints">
+
+
+
+ <h3><span class="secno"><span class="delete">5.1</span><span class="insert">6.1</span> </span>Uniqueness Constraints</h3>
+
+
+
+ <p> In the absence of existential variables, uniqueness constraints
+ could be checked directly by checking that no identifier appears
+ more than once for a given statement. However, in the presence of
+ existential variables, we need to be more careful to combine
+ partial information that might be present in multiple compatible
+ statements, due to inferences. Uniqueness constraints are
+ enforced through <a href="#dfn-merging" class="internalDFN">merging</a> pairs of statements subject to
+ equalities. For example, suppose we have two activity statements
+ <span class="name">activity(a,2011-11-16T16:00:00,_t1,[a=1])</span> and <span class="name">activity(a,_t2,2011-11-16T18:00:00,[b=2])</span>, with existential variables <span class="name">_t1</span> and <span class="name">_t2</span>. The <a>merge</a> of
+ these two statements (describing the same activity <span class="name">a</span>) is <span class="name">activity(a,2011-11-16T16:00:00,2011-11-16T18:00:00,[a=1,b=2])</span>. </p>
+
+ <span class="delete">Merging</span><span class="delete"> is an operation that can be applied
+ to a pair of terms, or a pair of attribute lists.
+ The result of merging is either a substitution (mapping
+ existentially quantified variables to terms) or failure, indicating that the merge
+ cannot be performed. Merging of pairs of terms, attribute lists,
+ or statements is defined as follows.</span>
+
+
+ <span class="delete"> If </span><span class="delete">t</span><span class="delete"> and </span><span class="delete">t'</span><span class="delete"> are constant identifiers or values
+ (including the placeholder </span><span class="delete">-</span><span class="delete">), then
+ their </span><span class="delete">merge</span><span class="delete"> exists only if they are equal, otherwise merging
+fails. </span>
+ <span class="delete"> If </span><span class="delete">x</span><span class="delete"> is an existential variable
+ and
+ </span><span class="delete">t'</span><span class="delete"> is any term (identifier, constant,
+ placeholder </span><span class="delete">-</span><span class="delete">, or
+ existential variable), then their
+ </span><span class="delete">merge</span><span class="delete"> is </span><span class="delete">t'</span><span class="delete">, and the resulting substitution is
+ </span><span class="delete">[x=t']</span><span class="delete">. In the special case where </span><span class="delete">t'=x</span><span class="delete">, the merge is
+ </span><span class="delete">x</span><span class="delete"> and the resulting substitution is empty.</span>
+ <span class="delete"> If </span><span class="delete">t</span><span class="delete"> is any term (identifier, constant,
+ placeholder </span><span class="delete">-</span><span class="delete">, or
+ existential variable) and
+ </span><span class="delete">x'</span><span class="delete"> is an existential variable, then their
+ merge is the same as the merge of </span><span class="delete">x</span><span class="delete"> and </span><span class="delete">t</span><span class="delete">.</span>
+ <span class="delete"> The </span><span class="delete">merge</span><span class="delete"> of two attribute lists </span><span class="delete">attrs1</span><span class="delete"> and </span><span class="delete">attrs2</span><span class="delete">
+ is their union, considered as sets of key-value pairs, written </span><span class="delete">attrs1 ∪ attrs2</span><span class="delete">. Duplicate keys with
+ different are
+ allowed, but equal key-value pairs are merged.</span>
+
+
+
+<span class="delete">Merging for terms is analogous to unification in
+ logic programming and theorem proving, restricted to flat terms with
+ no function symbols. No occurs check is needed because there are no
+ function symbols.</span>
+
+
+
+
+ <p>
+A typical uniqueness constraint is as follows:
+ </p>
+ <div class="constraint-example" id="uniqueness-example"><div class="ruleTitle"><a class="internalDFN" href="#uniqueness-example">Constraint-example NNN (uniqueness-example)</a></div>
+<p> <span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span> <span class="conditional">THEN</span> <span class="name">t<sub>1</sub></span> = <span class="name">u<sub>1</sub></span> and ... and <span class="name">t<sub>n</sub></span> = <span class="name">u<sub>n</sub></span>.</p>
+ </div>
+
+ <p> Such a constraint is enforced as follows:</p>
+ <ol> <li>Suppose PROV instance <span class="math">I</span> contains all of the hypotheses
+ <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span>.
+ </li>
+ <li>Attempt to <span class="delete">merge</span><span class="insert">unify</span> all of the equated terms in the conclusion
+ <span class="name">t<sub>1</sub></span> = <span class="name">u<sub>1</sub></span> and ... and <span class="name">t<sub>n</sub></span> = <span class="name">u<sub>n</sub></span>.
+ </li>
+ <li>If <span class="delete">merging</span><span class="insert">unification</span> fails, then the constraint
+ is unsatisfiable, so application of the constraint to <span class="math">I</span>
+ fails. If this failure occurs during <a>normalization</a> prior to
+validation, then <span class="math">I</span> is invalid, as explained in <a href="#normalization-validity-equivalence">Section 6</a>.
+ </li>
+ <li>If <span class="delete">merging</span><span class="insert">unification</span> succeeds with a substitution <span class="math">S</span>, then
+ <span class="math">S</span> is applied to the instance <span class="math">I</span>, yielding result <span class="math">S(I)</span>.</li>
+ </ol>
+
+<p> <em><dfn id="dfn-key-constraints">Key constraints</dfn></em> are uniqueness constraints
+ that specify that a particular key field of a relation uniquely
+ determines the other parameters. Key constraints are written as follows:
+ </p>
+
+ <div class="constraint-example" id="key-example"><div class="ruleTitle"><a class="internalDFN" href="#key-example">Constraint-example NNN (key-example)</a></div>
+ <p>The <span class="name">a<sub>k</sub></span> field is a <span class="conditional">KEY</span> for relation <span class="name">r(a<sub>0</sub>; a<sub>1</sub>,...,a<sub>n</sub>)</span>. </p></div>
+
+ <p> Because of the presence of attributes, key constraints do not
+ reduce directly to uniqueness constraints. Instead, we enforce key
+ constraints <span class="delete">as follows.</span><span class="insert">using the following </span><dfn id="dfn-merging"><span class="insert">merging</span></dfn><span class="insert"> process.</span> </p>
+ <ol>
+ <li> Suppose <span class="name">r(a<sub>0</sub>; a<sub>1</sub>,...a<sub>n</sub>,attrs1)</span> and <span class="name">r(b<sub>0</sub>; b<sub>1</sub>,...b<sub>n</sub>,attrs2)</span> hold in PROV instance <span class="math">I</span>, where the key fields <span class="name">a<sub>k</sub> = b<sub>k</sub></span> are equal.</li>
+ <li> Attempt to <span class="delete">merge</span><span class="insert">unify</span> all of the corresponding parameters <span class="name">a<sub>0</sub> = b<sub>0</sub> </span> and ... and <span class="name">a<sub>n</sub> = b<sub>n</sub></span>.
+ </li>
+ <li>If <span class="delete">merging</span><span class="insert">unification</span> fails, then the constraint is unsatisfiable, so
+ application of the key constraint to <span class="math">I</span> fails.
+ </li>
+ <li>If <span class="delete">merging</span><span class="insert">unification</span> succeeds with substitution <span class="math">S</span>, then we remove <span class="name">r(a<sub>0</sub>; a<sub>1</sub>,...a<sub>n</sub>,attrs1)</span> and <span class="name">r(b<sub>0</sub>; b<sub>1</sub>,...b<sub>n</sub>,attrs2)</span> from <span class="math">I</span>, obtaining
+ instance <span class="math">I'</span>, and return instance <span class="name">{r(S(a<sub>0</sub>); S(a<sub>1</sub>),...S(a<sub>n</sub>),attrs1 ∪
+ attrs2)}</span> ∪ <span class="math">S(I')</span>.
+ </li></ol>
+
+
+
+
+
+
+<p>Thus, if a PROV instance contains an apparent violation of a uniqueness
+ constraint or key constraint,<span class="insert"> unification or</span> merging can be used to determine
+ whether the constraint can be satisfied by instantiating some existential
+ variables with other terms. For key constraints, this is the same
+ as merging pairs of statements whose keys are equal and whose
+ corresponding arguments are compatible, because after
+ <span class="delete">merging</span><span class="insert">unifying</span> respective arguments and<span class="insert"> combining</span> attribute lists, the two statements
+ become equal and one can be omitted. </p>
+
+
+
+
+
+
+<p>
+</p><hr>
+
+ <p id="key-object_text">The various identified objects of PROV <em class="rfc2119" title="must">must</em> have
+ unique statements describing them within a valid PROV instance.
+ This is enforced through
+ the following key constraints:
+ </p>
+ <div class="constraint" id="key-object"><div class="ruleTitle"><a class="internalDFN" href="#key-object">Constraint <span class="delete">23</span><span class="insert">22</span> (key-object)</a></div>
+<p></p><ol>
+ <li>The identifier field <span class="delete">e</span><a href="http://www.w3.org/TR/prov-dm/#entity.id"><span class="name"><span class="insert">id</span></span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name"><span class="delete">entity(e,attrs)</span><span class="insert">entity(id,attrs)</span></span> statement.
+ </li>
+ <li>The identifier field <span class="delete">a</span><a href="http://www.w3.org/TR/prov-dm/#activity.id"><span class="name"><span class="insert">id</span></span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name"><span class="delete">activity(a,t1,t2,attrs)</span><span class="insert">activity(id,t1,t2,attrs)</span></span> statement.
+ </li>
+<li>The identifier field <span class="delete">ag</span><a href="http://www.w3.org/TR/prov-dm/#agent.id"><span class="name"><span class="insert">id</span></span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name"><span class="delete">agent(ag,attrs)</span><span class="insert">agent(id,attrs)</span></span> statement.
+ </li>
+ </ol>
+ </div>
+
+ <hr>
+ <p id="key-properties_text"> Likewise, the statements
+in a valid PROV instance must provide consistent information about
+ each identified object or relationship. The following key
+ constraints require that all of the information about each identified
+ statement can be merged into a single, consistent statement:
+ </p>
+ <div class="constraint" id="key-properties"><div class="ruleTitle"><a class="internalDFN" href="#key-properties">Constraint <span class="delete">24</span><span class="insert">23</span> (key-properties)</a></div>
+<p></p><ol>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#generation.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasGeneratedBy(id; e,a,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#usage.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">used(id; a,e,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#communication.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasInformedBy(id; a2,a1,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#start.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasStartedBy(id; a2,e,a1,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#end.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasEndedBy(id; a2,e,a1,t,attrs)</span> statement.
+ </li>
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#invalidation.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasInvalidatedBy(id; e,a,t,attrs)</span> statement.
+ </li>
+ <li><span class="insert">The identifier field </span><a href="http://www.w3.org/TR/prov-dm/#derivation.id"><span class="name"><span class="insert">id</span></span></a><span class="insert"> is a </span><span class="conditional"><span class="insert">KEY</span></span><span class="insert"> for
+ the </span><span class="name"><span class="insert">wasDerivedFrom(id; e2, e1, a, g2, u1, attrs)</span></span><span class="insert"> statement.
+ </span></li>
+ <li><span class="insert">The identifier field </span><a href="http://www.w3.org/TR/prov-dm/#attribution.id"><span class="name"><span class="insert">id</span></span></a><span class="insert"> is a </span><span class="conditional"><span class="insert">KEY</span></span><span class="insert"> for
+ the </span><span class="name"><span class="insert">wasAttributedTo(id; e,ag,attr)</span></span><span class="insert"> statement.
+ </span></li>
+ <li><span class="insert">The identifier field </span><a href="http://www.w3.org/TR/prov-dm/#association.id"><span class="name"><span class="insert">id</span></span></a><span class="insert"> is a </span><span class="conditional"><span class="insert">KEY</span></span><span class="insert"> for
+ the </span><span class="name"><span class="insert">wasAssociatedWith(id; a,ag,pl,attrs)</span></span><span class="insert"> statement.
+ </span></li>
+
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#delegation.id"><span class="name">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name"><span class="delete">wasDerivedFrom(id; e2, e1, a, g2, u1, attrs)</span><span class="insert">actedOnBehalfOf(id; ag2,ag1,a,attrs)</span></span> statement.
+ </li>
+
+ <li>The identifier field <a href="http://www.w3.org/TR/prov-dm/#influence.id"><span class="name">id</span><span class="delete"> is a </span><span class="delete">KEY</span><span class="delete"> for
+ the </span><span class="delete">wasAttributedTo(id; e,ag,attr)</span><span class="delete"> statement.
+ </span>
+ <span class="delete">The identifier field </span><span class="delete">id</span><span class="delete"> is a </span><span class="delete">KEY</span><span class="delete"> for
+ the </span><span class="delete">wasAssociatedWith(id; a,ag,pl,attrs)</span><span class="delete"> statement.
+ </span>
+ <span class="delete">The identifier field </span><span class="delete">id</span><span class="delete"> is a </span><span class="delete">KEY</span><span class="delete"> for
+ the </span><span class="delete">wasAssociatedWith(id; a,ag,-,attrs)</span><span class="delete"> statement.
+ </span>
+ <span class="delete">The identifier field </span><span class="delete">id</span><span class="delete"> is a </span><span class="delete">KEY</span><span class="delete"> for
+ the </span><span class="delete">actedOnBehalfOf(id; ag2,ag1,a,attrs)</span><span class="delete"> statement.
+ </span>
+ <span class="delete">The identifier field </span><span class="delete">id</span></a> is a <span class="conditional">KEY</span> for
+ the <span class="name">wasInfluencedBy(id; o2,o1,attrs)</span> statement.
+ </li>
+</ol>
+ </div>
+
+
+
+<hr>
+
+
+<div id="unique-generation_text">
+<p> Entities may have multiple generation or invalidation events
+ (either or both may, however, be left implicit). An entity can be
+ generated by more than one activity, with one generation event per
+ each entity-activity pair. These events must be simultaneous, as required by <a class="rule-ref" href="#generation-generation-ordering"><span>Constraint <span class="delete">41</span><span class="insert">39</span> (generation-generation-ordering)</span></a>
+ and <a class="rule-ref" href="#invalidation-invalidation-ordering"><span>Constraint <span class="delete">42</span><span class="insert">40</span> (invalidation-invalidation-ordering)</span></a>.
+
+</p>
+</div>
+
+
+<div class="constraint" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint <span class="delete">25</span><span class="insert">24</span> (unique-generation)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasGeneratedBy(gen1; e,a,_t1,_attrs1)</span> and <span class="name">wasGeneratedBy(gen2; e,a,_t2,_attrs2)</span>,
+<span class="conditional">THEN</span> <span class="name">gen1</span> = <span class="name">gen2</span>.</p>
+</div>
+
+<p>
+
+</p><hr>
+<p id="unique-invalidation_text">
+
+</p><div class="constraint" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint <span class="delete">26</span><span class="insert">25</span> (unique-invalidation)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasInvalidatedBy(inv1; e,a,_t1,_attrs1)</span> and <span class="name">wasInvalidatedBy(inv2; e,a,_t2,_attrs2)</span>,
+<span class="conditional">THEN</span> <span class="name">inv1</span> = <span class="name">inv2</span>.</p>
+</div>
+
+
+<div class="remark"> <p> It follows from the above uniqueness and key
+ constraints that the generation and invalidation events linking an
+ entity and activity are unique, if specified. However, because we
+ apply the constraints by merging, it is possible for a valid PROV instance
+to contain multiple statements about the same generation or
+ invalidation event, for example:</p>
+ <pre>wasGeneratedBy(id1; e,a,-,[prov:location="Paris"])
+wasGeneratedBy(-; e,a,-,[color="Red"])
+</pre>
+<p> When the uniqueness and key constraints are applied, the instance is
+ <a title="normal form" href="#dfn-normal-form" class="internalDFN">normalized</a> to the following form:</p>
+ <pre>wasGeneratedBy(id1; e,a,_t,[prov:location="Paris",color="Red"])
+</pre>
+<p>
+ where <span class="name">_t</span> is a new existential variable.
+ </p>
+</div>
+
+
+<hr>
+<p id="unique-wasStartedBy_text">
+An activity may have more than one start and
+end event, each having a different activity (either or both may,
+however, be left implicit). However,
+the triggering entity linking any two activities in a start or end event is unique.
+That is, an activity may be started by
+several other activities, with shared or separate triggering
+entities. If an activity is started or ended by multiple events, they must all
+be simultaneous, as specified in <a class="rule-ref" href="#start-start-ordering"><span>Constraint <span class="delete">33</span><span class="insert">31</span> (start-start-ordering)</span></a>
+and <a class="rule-ref" href="#end-end-ordering"><span>Constraint <span class="delete">34</span><span class="insert">32</span> (end-end-ordering)</span></a>.
+</p>
+
+<div class="constraint" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint <span class="delete">27</span><span class="insert">26</span> (unique-wasStartedBy)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasStartedBy(start1; a,_e1,a0,_t1,_attrs1)</span> and <span class="name">wasStartedBy(start2; a,_e2,a0,_t2,_attrs2)</span>, <span class="conditional">THEN</span> <span class="name">start1</span> = <span class="name">start2</span>.</p>
+</div>
+
+<p id="unique-wasEndedBy_text">
+
+</p><div class="constraint" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint <span class="delete">28</span><span class="insert">27</span> (unique-wasEndedBy)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">wasEndedBy(end1; a,_e1,a0,_t1,_attrs1)</span> and <span class="name">wasEndedBy(end2; a,_e2,a0,_t2,_attrs2)</span>, <span class="conditional">THEN</span> <span class="name">end1</span> = <span class="name">end2</span>.</p>
+</div>
+
+
+<hr>
+
+
+
+
+
+ <p id="unique-startTime_text">An <a href="#dfn-start-event" class="internalDFN">activity start event</a> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity starts. It allows for an optional time attribute. <span id="optional-start-time">Activities also allow for an optional start time attribute. If both are specified, they <em class="rfc2119" title="must">must</em> be the same, as expressed by the following constraint.</span>
+</p>
+
+<div class="constraint" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint <span class="delete">29</span><span class="insert">28</span> (unique-startTime)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">activity(a2,t1,_t2,_attrs)</span> and <span class="name">wasStartedBy(_start; a2,_e,_a1,t,_attrs)</span>, <span class="conditional">THEN</span> <span class="name">t1</span>=<span class="name">t</span>.</p>
+</div>
+
+<hr>
+
+<p id="unique-endTime_text">An <a href="#dfn-end-event" class="internalDFN">activity end event</a> is the <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> that marks the instant an activity ends. It allows for an optional time attribute. <span id="optional-end-time">Activities also allow for an optional end time attribute. If both are specified, they <em class="rfc2119" title="must">must</em> be the same, as expressed by the following constraint.</span>
+</p>
+
+<div class="constraint" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint <span class="delete">30</span><span class="insert">29</span> (unique-endTime)</a></div>
+<p>
+<span class="conditional">IF</span> <span class="name">activity(a2,_t1,t2,_attrs)</span> and <span class="name">wasEndedBy(_end; a2,_e,_a1,t,_attrs1)</span>, <span class="conditional">THEN</span> <span class="name">t2</span> = <span class="name">t</span>.</p>
+</div>
+
+<p>
+
+
+</p><hr>
+
+
+
+<span class="delete">Note: The following constraint is associated with a feature "</span><span class="delete">at risk</span><span class="delete">" and may be removed from this specification based on feedback. Please send feedback to public-prov-comments@w3.org.</span>
+
+
+
+
+<span class="delete">An entity can be the subject of at most one mention relation.</span>
+
+
+
+<span class="delete">Constraint 31 (unique-mention)</span>
+
+<span class="delete">IF</span> <span class="delete">mentionOf(e, e1, b1)</span><span class="delete"> and </span><span class="delete">mentionOf(e, e2, b2)</span><span class="delete">,
+</span><span class="delete">THEN</span> <span class="delete">e1</span><span class="delete">=</span><span class="delete">e2</span><span class="delete"> and </span><span class="delete">b1</span><span class="delete">=</span><span class="delete">b2</span><span class="delete">.</span>
+
+
+
+
+
+
+
+
+
+
+
+
+
+</section>
+
+<section id="event-ordering-constraints">
+<h3><span class="secno"><span class="delete">5.2</span><span class="insert">6.2</span> </span>Event Ordering Constraints</h3>
+
+
+<p>Given that provenance consists of a description of past entities
+and activities, <a href="#dfn-valid" class="internalDFN">valid</a> provenance instances <em class="rfc2119" title="must">must</em>
+satisfy <em>ordering constraints</em> between instantaneous events, which are introduced in
+this section. For instance, an entity can only be used after it was
+generated; in other words, an entity's <a title="entity generation
+event" href="#dfn-generation-event" class="internalDFN">generation event</a> precedes any of this
+entity's <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage events</a>. Should this
+ordering constraint be violated, the associated generation and
+usage would not be credible. The rest of this section defines
+the <dfn id="dfn-temporal-interpretation">temporal interpretation</dfn> of provenance instances as a
+set of instantaneous event ordering constraints. </p>
+
+
+<p>To allow for minimalistic clock assumptions, like Lamport
+[<cite><a class="bibref" href="#bib-CLOCK">CLOCK</a></cite>], PROV relies on a notion of relative ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a>,
+without using physical clocks. This specification assumes that a <a href="#dfn-preorder" class="internalDFN">preorder</a> exists between <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a>.
+</p>
+
+
+<p>Specifically, <dfn id="dfn-precedes">precedes</dfn> is a <a href="#dfn-preorder" class="internalDFN">preorder</a>
+between <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a>. A
+constraint of the form
+<span class="name">e1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a> <span class="name">e2</span> means that <span class="name">e1</span>
+happened at the same time as or before <span class="name">e2</span>.
+For symmetry, <dfn id="dfn-follows">follows</dfn> is defined as the
+inverse of <a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>; that is, a constraint of
+the form
+<span class="name">e1</span> follows <span class="name">e2</span> means that <span class="name">e1</span> happened at the same time
+as or after <span class="name">e2</span>. Both relations are
+<a href="#dfn-preorder" class="internalDFN">preorder</a>s, meaning that they are <a href="#dfn-reflexive" class="internalDFN">reflexive</a> and
+<a href="#dfn-transitive" class="internalDFN">transitive</a>. Moreover, we sometimes consider <em>strict</em> forms of these
+orders: we say <span class="name">e1</span> <dfn id="dfn-strictly-precedes">strictly precedes</dfn> <span class="name">e2</span> to indicate that <span class="name">e1</span>
+happened before <span class="name">e2</span>, but not at the same time. This is a
+<a href="#dfn-transitive" class="internalDFN">transitive</a><span class="insert">, </span><a href="#dfn-irreflexive" class="internalDFN"><span class="insert">irreflexive</span></a> relation. </p>
+
+
+<p>PROV also allows for time observations to be inserted in
+specific provenance statements, for each of the five kinds of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a> introduced in
+this specification. Times in provenance records arising from
+different sources might be with respect to different timelines
+(e.g. different time zones) leading to apparent inconsistencies. For
+the purpose of checking ordering constraints, the times associated
+with events are irrelevant; thus, there is no inference that time ordering
+implies event ordering, or vice versa. However, an application <em class="rfc2119" title="may">may</em> flag time values
+that appear inconsistent with the event ordering as possible
+inconsistencies. When generating provenance, an application <em class="rfc2119" title="should">should</em>
+use a consistent <span class="delete">imeline</span><span class="insert">timeline</span> for related PROV statements within an
+instance.</p>
+
+
+<p> A typical ordering constraint is as follows.</p>
+
+ <div class="constraint-example" id="ordering-example"><div class="ruleTitle"><a class="internalDFN" href="#ordering-example">Constraint-example NNN (ordering-example)</a></div>
+ <p><span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span> <span class="conditional">THEN</span> <span class="name">evt1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a>/<a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a> <span class="name">evt2</span>. </p></div>
+ <p>
+ The conclusion of an ordering constraint is either <a href="#dfn-precedes" class="internalDFN">precedes</a>
+ or <a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a>. One way to check
+ ordering constraints is to
+ generate all <a href="#dfn-precedes" class="internalDFN">precedes</a> and <a title="precedes" href="#dfn-precedes" class="internalDFN">strictly
+ precedes</a>
+ relationships arising from the ordering constraints to form a directed graph, with edges marked <a href="#dfn-precedes" class="internalDFN">precedes</a> or
+ <a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a>, and check that there is no cycle
+ containing a <a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a> edge.
+ </p>
+
+
+
+
+
+<section id="activity-constraints">
+<h4><span class="secno"><span class="delete">5.2.1</span><span class="insert">6.2.1</span> </span>Activity constraints</h4>
+
+<p>
+This section specifies ordering constraints from the perspective of
+the <a href="#lifetime" class="internalDFN">lifetime</a> of an activity. An activity starts, then during
+its lifetime can use, generate or invalidate entities, communicate
+ with, start, or end
+other
+activities, or be associated with agents, and finally it ends. The following constraints amount to
+checking that all of the events associated with an activity take place
+within the activity's lifetime, and the start and end events mark the
+start and endpoints of its lifetime.
+</p>
+
+<p><a href="#ordering-activity" class="fig-ref">Figure 3</a> summarizes the ordering
+ constraints on activities in a
+graphical manner. For this and subsequent figures, an event time line points to the
+right. Activities are represented by rectangles, whereas entities are
+represented by circles. Usage, generation and invalidation are
+represented by the corresponding edges between entities and
+activities. The five kinds of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous events</a> are represented by vertical
+dotted lines (adjacent to the vertical sides of an activity's
+rectangle, or intersecting usage and generation edges). The ordering
+constraints are represented by triangles: an occurrence of a triangle between two <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> vertical dotted lines represents that the event denoted by the left
+line precedes the event denoted by the right line.</p>
+ <span class="delete"> Miscellaneous suggestions about figures
+ (originally from Tim Lebo):
+</span>
+ <span class="delete">
+ I think it would help if the "corresponding edges between entities and activities" where the same visual style as the vertical line marking the time the Usage, generation and derivation occurred. A matching visual style provides a Gestalt that matches the concept. I am looking at subfigures b and c in 5.2. </span>
+
+
+
+
+
+
+ <div style="text-align: center;">
+
+<span class="figure" id="ordering-activity">
+<img src="images/constraints/ordering-activity.png" alt="constraints between events">
+<br>
+<span class="figcaption" id="ordering-activity-fig">Figure 3<sup><a class="internalDFN" href="#ordering-activity-fig"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering constraints for activities</span>
+</span>
+</div>
+
+
+
+<hr>
+
+<p id="start-precedes-end_text">
+The existence of an activity implies that the <a href="#dfn-start-event" class="internalDFN">activity start
+event</a> always <a href="#dfn-precedes" class="internalDFN">precedes</a> the corresponding <a href="#dfn-end-event" class="internalDFN">activity end
+event</a>. This is illustrated by
+<a href="#ordering-activity" class="fig-ref">Figure 3</a>
+(a) and expressed by <a class="rule-ref" href="#start-precedes-end"><span>Constraint <span class="delete">32</span><span class="insert">30</span> (start-precedes-end)</span></a>.</p>
+
+<div class="constraint" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint <span class="delete">32</span><span class="insert">30</span> (start-precedes-end)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">wasStartedBy(start; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+</p>
+</div>
+<p>
+
+</p><hr>
+
+<p id="start-start-ordering_text">
+If an activity is started by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two start
+events that start the same activity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other.
+</p>
+<div class="constraint" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint <span class="delete">33</span><span class="insert">31</span> (start-start-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasStartedBy(start1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasStartedBy(start2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">start2</span>.
+ </p>
+</div>
+
+<hr>
+
+<p id="end-end-ordering_text">
+If an activity is ended by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two end
+events that end the same activity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other, that is, they are simultaneous.
+</p>
+<div class="constraint" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint <span class="delete">34</span><span class="insert">32</span> (end-end-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasEndedBy(end1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">end1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </p>
+</div>
+
+<hr>
+
+<p id="usage-within-activity_text">A usage implies ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since the <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage event</a> had to occur during the associated activity. This is
+illustrated by <a href="#ordering-activity" class="fig-ref">Figure 3</a> (b) and expressed by <a class="rule-ref" href="#usage-within-activity"><span>Constraint <span class="delete">35</span><span class="insert">33</span> (usage-within-activity)</span></a>.</p>
+
+<div class="constraint" id="usage-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#usage-within-activity">Constraint <span class="delete">35</span><span class="insert">33</span> (usage-within-activity)</a></div>
+<ol>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">wasStartedBy(start; a,_e1,_a1,_t1,_attrs1)</span>
+ and
+<span class="name">used(use; a,_e2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">use</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">used(use; a,_e1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">use</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+ </li>
+ </ol>
+</div>
+
+<p>
+
+</p><hr>
+
+
+<p id="generation-within-activity_text">A generation implies ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since the <a title="entity generation event" href="#dfn-generation-event" class="internalDFN">generation event</a> had to occur during the associated activity. This is
+illustrated by <a href="#ordering-activity" class="fig-ref">Figure 3</a> (c) and expressed by <a class="rule-ref" href="#generation-within-activity"><span>Constraint <span class="delete">36</span><span class="insert">34</span> (generation-within-activity)</span></a>.</p>
+
+<div class="constraint" id="generation-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#generation-within-activity">Constraint <span class="delete">36</span><span class="insert">34</span> (generation-within-activity)</a></div>
+ <ol>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">wasStartedBy(start; a,_e1,_a1,_t1,_attrs1)</span>
+ and
+<span class="name">wasGeneratedBy(gen; _e2,a,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen</span>.
+ </li>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; _e,a,_t,_attrs)</span>
+and
+<span class="name">wasEndedBy(end; a,_e1,_a1,_t1,_attrs1)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+ </li>
+ </ol>
+</div>
+
+<p>
+
+</p><hr>
+<p id="wasInformedBy-ordering_text">
+Communication between two activities <span class="name">a1</span>
+and <span class="name">a2</span> also implies ordering
+of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since some entity must
+have been generated by the former and used by the latter, which
+implies that the start event of <span class="name">a1</span> cannot
+follow the end event of <span class="name">a2</span>. This is
+illustrated by
+<a href="#ordering-activity" class="fig-ref">Figure 3</a>
+(d) and expressed by <a class="rule-ref" href="#wasInformedBy-ordering"><span>Constraint <span class="delete">37</span><span class="insert">35</span> (wasInformedBy-ordering)</span></a>.</p>
+
+<div class="constraint" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint <span class="delete">37</span><span class="insert">35</span> (wasInformedBy-ordering)</a></div>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasInformedBy(_id; a2,a1,_attrs)</span>
+and
+<span class="name">wasStartedBy(start; a1,_e1,_a1',_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end; a2,_e2,_a2',_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+</p>
+</div>
+<p>
+
+
+
+</p></section>
+
+<section id="entity-constraints">
+<h4><span class="secno"><span class="delete">5.2.2</span><span class="insert">6.2.2</span> </span> Entity constraints</h4>
+
+
+
+
+
+
+
+<p><span class="insert">
+As with activities, entities have lifetimes: they are generated, then
+can be used, other entities can be derived from them, and finally they
+can be invalidated. </span>The <span class="delete">figure(s)</span><span class="insert">constraints on these events are
+illustrated graphically</span> in <span class="delete">this section should have vertical lines with visual styles that match the diagonal arrow that they go with. </span>
+
+<span class="delete">
+As with activities, entities have lifetimes: they are generated, then
+can be used, other entities can be derived from them, and finally they
+can be invalidated. The constraints on these events are
+illustrated graphically in </span><a href="#ordering-entity" class="fig-ref">Figure 4</a> and
+<a href="#ordering-entity-trigger" class="fig-ref">Figure 5</a>.
+</p>
+
+
+
+<div style="text-align: center;">
+<span class="figure" id="ordering-entity">
+<img src="images/constraints/ordering-entity.png" alt="ordering constraints for entities">
+<br>
+<span class="figcaption" id="ordering-entity-fig">Figure 4<sup><a class="internalDFN" href="#ordering-entity-fig"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering constraints for entities</span></span>
+</div>
+
+<p>
+
+</p><hr>
+
+<p id="generation-precedes-invalidation_text">
+Generation of an entity precedes its invalidation. (This
+follows from other constraints if the entity is used, but it is stated
+explicitly here to cover the case of an entity that is generated and
+invalidated without being used.)</p>
+
+<div class="constraint" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint <span class="delete">38</span><span class="insert">36</span> (generation-precedes-invalidation)</a></div>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.
+</p>
+</div>
+
+
+
+
+<hr>
+
+<p id="generation-precedes-usage_text">
+A usage and a generation for a given entity implies ordering of <a title="instantaneous event" href="#dfn-event" class="internalDFN">events</a>, since the <a title="entity generation
+event" href="#dfn-generation-event" class="internalDFN">generation event</a> had to precede the <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage event</a>. This is
+illustrated by <a href="#ordering-entity" class="fig-ref">Figure 4</a>(a) and expressed by <a class="rule-ref" href="#generation-precedes-usage"><span>Constraint <span class="delete">39</span><span class="insert">37</span> (generation-precedes-usage)</span></a>.</p>
+
+<div class="constraint" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint <span class="delete">39</span><span class="insert">37</span> (generation-precedes-usage)</a></div>
+<p> <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">used(use; _a2,e,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">use</span>.
+</p>
+</div>
+
+
+<hr>
+
+<p id="usage-precedes-invalidation_text">All usages of an entity precede its invalidation, which is captured by <a class="rule-ref" href="#usage-precedes-invalidation"><span>Constraint <span class="delete">40</span><span class="insert">38</span> (usage-precedes-invalidation)</span></a> (without any explicit graphical representation).</p>
+
+<div class="constraint" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint <span class="delete">40</span><span class="insert">38</span> (usage-precedes-invalidation)</a></div>
+<p>
+<span class="conditional">IF</span>
+<span class="name">used(use; _a1,e,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">use</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.</p>
+</div>
+
+
+
+
+<hr>
+
+<p id="generation-generation-ordering_text">
+If an entity is generated by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two generation
+events that generate the same entity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other.
+</p>
+<div class="constraint" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint <span class="delete">41</span><span class="insert">39</span> (generation-generation-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen1; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasGeneratedBy(gen2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+ </p>
+</div>
+
+<hr>
+
+<p id="invalidation-invalidation-ordering_text">
+If an entity is invalidated by more than one activity, the events must all
+be simultaneous. The following constraint requires that if there are two invalidation
+events that invalidate the same entity, then one <a href="#dfn-precedes" class="internalDFN">precedes</a> the
+other. Using this constraint in both directions means that each event
+<a href="#dfn-precedes" class="internalDFN">precedes</a> the other, that is, they are simultaneous.
+</p>
+<div class="constraint" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint <span class="delete">42</span><span class="insert">40</span> (invalidation-invalidation-ordering)</a></div>
+ <p>
+ <span class="conditional">IF</span>
+<span class="name">wasInvalidatedBy(inv1; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">inv1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv2</span>.
+ </p>
+</div>
+
+
+
+<p id="derivation-usage-generation-ordering_text">If there is a
+derivation relationship linking <span class="name">e2</span> and <span class="name">e1</span>, then
+this means that the entity <span class="name">e1</span> had some influence on the entity <span class="name">e2</span>; for this to be possible, some event ordering must be satisfied.
+First, we consider derivations, where the activity and usage are known. In that case, the <a title="entity usage event" href="#dfn-usage-event" class="internalDFN">usage</a> of <span class="name">e1</span> has to precede the <a title="entity generation
+event" href="#dfn-generation-event" class="internalDFN">generation</a> of <span class="name">e2</span>.
+This is
+illustrated by <a href="#ordering-entity-fig">Figure 4</a> (b) and expressed by <a class="rule-ref" href="#derivation-usage-generation-ordering"><span>Constraint <span class="delete">43</span><span class="insert">41</span> (derivation-usage-generation-ordering)</span></a>.</p>
+
+
+<div class="constraint" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint <span class="delete">43</span><span class="insert">41</span> (derivation-usage-generation-ordering)</a></div>
+ <p>
+ In this constraint, <span class="name">_a</span>, <span class="name">gen2</span>, <span class="name">use1</span> <em class="rfc2119" title="must not">must not</em> be placeholders.</p>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasDerivedFrom(_d; _e2,_e1,_a,gen2,use1,_attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">use1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+</p>
+</div>
+<p>
+</p><hr>
+
+<p id="derivation-generation-generation-ordering_text">
+When the activity, generation or usage is unknown, a similar constraint exists, except that the constraint refers to its
+generation event, as
+illustrated by <a href="#ordering-entity-fig">Figure 4</a> (c) and expressed by <a class="rule-ref" href="#derivation-generation-generation-ordering"><span>Constraint <span class="delete">44</span><span class="insert">42</span> (derivation-generation-generation-ordering)</span></a>.</p>
+
+<div class="constraint" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint <span class="delete">44</span><span class="insert">42</span> (derivation-generation-generation-ordering)</a></div>
+ <p>
+In this constraint, any<span class="insert"> of</span> <span class="name">_a</span>, <span class="name">_g</span>, <span class="name">_u</span> <em class="rfc2119" title="may">may</em> be placeholders.</p>
+<p>
+ <span class="conditional">IF</span>
+<span class="name">wasDerivedFrom(_d; e2,e1,_a,_g,_u,attrs)</span>
+ and
+<span class="name">wasGeneratedBy(gen1; e1,_a1,_t1,_attrs1)</span>
+ and
+<span class="name">wasGeneratedBy(gen2; e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a href="#dfn-strictly-precedes" class="internalDFN">strictly precedes</a>
+<span class="name">gen2</span>.
+</p>
+ </div>
+
+<div class="remark">
+ <p>This constraint requires the derived
+ entity to be generated strictly following the generation of the
+ original entity. This follows from the [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>] definition of
+ derivation: <em>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</em>, thus
+ the derived entity must be newer than the original entity.</p>
+ <p>The event ordering is between generations of <span class="name">e1</span>
+and <span class="name">e2</span>, as opposed to derivation where usage is known,
+which implies ordering between the usage of <span class="name">e1</span> and
+generation of <span class="name">e2</span>. </p>
+</div>
+
+<hr>
+
+<p id="wasStartedBy-ordering_text">
+The entity that triggered the start of an activity must exist before the activity starts.
+This is
+illustrated by <a href="#ordering-entity-trigger" class="fig-ref">Figure 5</a>(a) and expressed by <a class="rule-ref" href="#wasStartedBy-ordering"><span>Constraint <span class="delete">45</span><span class="insert">43</span> (wasStartedBy-ordering)</span></a>.</p>
+
+
+<div class="constraint" id="wasStartedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-ordering">Constraint <span class="delete">45</span><span class="insert">43</span> (wasStartedBy-ordering)</a></div>
+ <ol>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasStartedBy(start; _a,e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">start</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasStartedBy(start; _a,e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.
+ </li>
+ </ol>
+</div>
+
+<hr>
+
+<p id="wasEndedBy-ordering_text"> Similarly, the entity that triggered
+the end of an activity must exist before the activity ends, as
+illustrated by
+<a href="#ordering-entity-trigger" class="fig-ref">Figure 5</a>(b).</p>
+
+
+<div class="constraint" id="wasEndedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-ordering">Constraint <span class="delete">46</span><span class="insert">44</span> (wasEndedBy-ordering)</a></div>
+ <ol>
+ <li>
+ <span class="conditional">IF</span>
+<span class="name">wasGeneratedBy(gen; e,_a1,_t1,_attrs1)</span>
+and
+ <span class="name">wasEndedBy(end; _a,e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasEndedBy(end; _a,e,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">end</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv</span>.
+ </li>
+ </ol>
+</div>
+
+<div style="text-align: center; ">
+<span class="figure" id="ordering-entity-trigger">
+<img src="images/constraints/ordering-entity-trigger.png" alt="ordering constraints for trigger entities">
+<br>
+<span class="figcaption" id="ordering-entity-trigger-fig">Figure 5<sup><a class="internalDFN" href="#ordering-entity-trigger-fig"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering constraints for trigger entities</span>
+</span>
+</div>
+
+<hr>
+<p id="specialization-generation-ordering_text">
+If an entity is a specialization of another, then the more
+specific entity must have been generated after the
+less specific entity was generated.
+</p>
+<div class="constraint" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint <span class="delete">47</span><span class="insert">45</span> (specialization-generation-ordering)</a></div>
+ <p>
+<span class="conditional">IF</span> <span class="name">specializationOf(e2,e1)</span> and <span class="name">wasGeneratedBy(gen1; e1,_a1,_t1,_attrs1)</span> and
+ <span class="name">wasGeneratedBy(gen2; e2,_a2,_t2,_attrs2)</span>
+ <span class="conditional">THEN</span> <span class="name">gen1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a> <span class="name">gen2</span>.
+</p></div>
+
+<p>
+
+</p><hr>
+<p id="specialization-invalidation-ordering_text">
+Similarly, if an entity is a specialization of another entity, and
+then
+the invalidation event of the more specific entity precedes that of
+the less specific entity.
+</p><div class="constraint" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint <span class="delete">48</span><span class="insert">46</span> (specialization-invalidation-ordering)</a></div>
+ <p>
+<span class="conditional">IF</span> <span class="name">specializationOf(e1,e2)</span> and
+ <span class="name">wasInvalidatedBy(inv1; e1,_a1,_t1,_attrs1)</span> and
+ <span class="name">wasInvalidatedBy(inv2; e2,_a2,_t2,_attrs2)</span>
+ <span class="conditional">THEN</span> <span class="name">inv1</span> <a href="#dfn-precedes" class="internalDFN">precedes</a> <span class="name">inv2</span>.
+</p>
+ </div>
+
+</section>
+
+<section id="agent-constraints">
+<h4><span class="secno"><span class="delete">5.2.3</span><span class="insert">6.2.3</span> </span> Agent constraints</h4>
+
+<p> Like entities and activities, agents have lifetimes that follow a
+familiar pattern. An agent that is also an entity can be generated
+and invalidated; an agent that is also an activity can be started or
+ended. During its lifetime, an agent can participate in interactions
+such as starting or ending other activities, association with an
+activity, attribution, or delegation.
+
+</p> <p>Further constraints associated with agents appear in <a href="#ordering-agents">Figure 6</a> and are discussed below.</p>
+
+<div style="text-align: center;">
+<span class="figure" id="ordering-agents-fig">
+<img src="images/constraints/ordering-agents.png" alt="ordering constraints for agents">
+<br>
+<span class="figcaption" id="ordering-agents">Figure 6<sup><a class="internalDFN" href="#ordering-agents"><span class="diamond"> ◊:</span></a></sup> Summary of <a title="instantaneous event" href="#dfn-event" class="internalDFN">instantaneous event</a> ordering
+ constraints for agents</span>
+</span>
+</div>
+
+<hr>
+
+
+<p id="wasAssociatedWith-ordering_text">An activity that was
+associated with an agent must have some overlap with the agent. The
+agent <em class="rfc2119" title="must">must</em> have been generated (or started), or <em class="rfc2119" title="must">must</em> have become
+associated with the activity, after the activity start: so, the agent <em class="rfc2119" title="must">must</em> exist before the activity end. Likewise, the agent may be destructed (or ended), or may terminate its association with the activity, before the activity end: hence, the agent invalidation (or end) is required to happen after the activity start.
+This is illustrated by <a href="#ordering-agents">Figure 6</a> (a) and expressed by <a class="rule-ref" href="#wasAssociatedWith-ordering"><span>Constraint <span class="delete">49</span><span class="insert">47</span> (wasAssociatedWith-ordering)</span></a>.</p>
+
+
+
+<div class="constraint" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAssociatedWith-ordering">Constraint <span class="delete">49</span><span class="insert">47</span> (wasAssociatedWith-ordering)</a></div>
+ <p>
+In the following inferences, <span class="name">_pl</span> <em class="rfc2119" title="may">may</em> be
+ a placeholder <span class="name">-</span>.
+ </p><ol> <li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv2; ag,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasGeneratedBy(gen1; ag,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; a,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; ag,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAssociatedWith(_assoc; a,ag,_pl,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; ag,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; a,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li>
+ </ol>
+</div>
+
+
+<p>
+
+</p><hr>
+
+<p id="wasAttributedTo-ordering_text">An agent to which an entity was attributed, <em class="rfc2119" title="must">must</em> exist before this entity was generated.
+This is
+illustrated by <a href="#ordering-agents">Figure 6</a> (b) and expressed by <a class="rule-ref" href="#wasAttributedTo-ordering"><span>Constraint <span class="delete">50</span><span class="insert">48</span> (wasAttributedTo-ordering)</span></a>.</p>
+
+
+
+
+<div class="constraint" id="wasAttributedTo-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAttributedTo-ordering">Constraint <span class="delete">50</span><span class="insert">48</span> (wasAttributedTo-ordering)</a></div>
+ <ol> <li>
+ <span class="conditional">IF</span>
+<span class="name">wasAttributedTo(_at; e,ag,_attrs)</span>
+and
+<span class="name">wasGeneratedBy(gen1; ag,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasGeneratedBy(gen2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">wasAttributedTo(_at; e,ag,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; ag,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasGeneratedBy(gen2; e,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">gen2</span>.
+ </li>
+ </ol>
+</div>
+
+<p>
+</p><hr>
+
+<p id="actedOnBehalfOf-ordering_text">For delegation, <span class="delete">two agents need</span><span class="insert">the responsible agent has</span> to <span class="insert">precede or </span>have some overlap <span class="delete">in their lifetime.</span><span class="insert">with the subordinate agent.</span></p>
+
+
+<div class="constraint" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a class="internalDFN" href="#actedOnBehalfOf-ordering">Constraint <span class="delete">51</span><span class="insert">49</span> (actedOnBehalfOf-ordering)</a></div>
+ <ol> <li>
+ <span class="conditional">IF</span>
+<span class="name">actedOnBehalfOf(_del; ag2,ag1,_a,_attrs)</span>
+and
+<span class="name">wasGeneratedBy(gen1; ag1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasInvalidatedBy(inv2; ag2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">gen1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">inv2</span>.
+ </li><li>
+ <span class="conditional">IF</span>
+<span class="name">actedOnBehalfOf(_del; ag2,ag1,_a,_attrs)</span>
+and
+<span class="name">wasStartedBy(start1; ag1,_e1,_a1,_t1,_attrs1)</span>
+and
+<span class="name">wasEndedBy(end2; ag2,_e2,_a2,_t2,_attrs2)</span>
+<span class="conditional">THEN</span>
+<span class="name">start1</span>
+<a title="precedes" href="#dfn-precedes" class="internalDFN">precedes</a>
+<span class="name">end2</span>.
+ </li>
+ </ol>
+
+</div>
+
+</section>
+
+</section>
+
+
+
+<section id="type-constraints">
+<h3><span class="secno"><span class="delete">5.3</span><span class="insert">6.3</span> </span>Type Constraints</h3>
+
+<p id="typing_text">The following <span class="delete">rule establishes</span><span class="insert">rules assign</span> types <span class="delete">denoted by</span><span class="insert">to</span> identifiers<span class="delete"> from</span><span class="insert">
+based on</span> their use within <span class="delete">expressions.</span><span class="insert">statements.</span>
+The function <span class="name">typeOf</span> gives the set of types denoted by an identifier.
+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 <span class="delete">term of</span><span class="insert">PROV statement, but a
+construct used only during validation</span> PROV, <span class="delete">but a construct introduced</span><span class="insert">similar</span> to <span class="delete">validate PROV statements.
+</span><a href="#dfn-precedes" class="internalDFN"><span class="insert">precedes</span></a><span class="insert">.
+</span></p>
+
+
+
+
+<p>
+ For any identifier <span class="name">id</span>, <span class="name">typeOf(id)</span> is a subset of {<span class="name">'entity'</span>, <span class="name">'activity'</span>, <span class="name">'agent'</span>, <span class="name">'prov:Collection'</span>, <span class="name">'prov:EmptyCollection'</span>}.
+For identifiers that do not have a type, <span class="name">typeOf</span> gives the empty set.
+ Identifiers can have more than one type, because of subtyping
+ (e.g. <span class="name">'prov:EmptyCollection'</span> is a subtype of <span class="name">'prov:Collection'</span>) or because certain types are not
+ disjoint (such as <span class="name">'agent'</span> and <span class="name">'entity'</span>). The set of types
+ does not reflect all of the distinctions among objects, only those
+ relevant for checking validity. In particular, <span class="delete">subtypes</span><span class="insert">a subtype</span> such as <span class="name">'plan'</span> <span class="delete">and </span><span class="delete">'bundle'</span><span class="delete"> are</span><span class="insert">is</span> omitted, and statements such as <span class="name">wasAssociatedWith</span> <span class="delete">and </span><span class="delete">mentionOf</span> that have plan<span class="delete"> or bundle</span> parameters only check that these parameters are entities.
+</p>
+
+<p>To check if a PROV instance satisfies type constraints, one obtains the types of identifiers by application of
+<a class="rule-ref" href="#typing"><span>Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</span></a>
+and check that none of the impossibility constraints
+<a class="rule-ref" href="#entity-activity-disjoint"><span>Constraint <span class="delete">57</span><span class="insert">55</span> (entity-activity-disjoint)</span></a> and
+<a class="rule-ref" href="#membership-empty-collection"><span>Constraint <span class="delete">58</span><span class="insert">56</span> (membership-empty-collection)</span></a> are
+ violated as a result.</p>
+
+
+<div class="constraint" id="typing"><div class="ruleTitle"><a class="internalDFN" href="#typing">Constraint <span class="delete">52</span><span class="insert">50</span> (typing)</a></div>
+
+
+<ol>
+<li>
+<span class="conditional">IF</span>
+ <span class="name">entity(e,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span>.
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">agent(ag,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'agent' ∈ typeOf(ag)</span>.
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">activity(a,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">used(u; a,e,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span> AND
+<span class="name">'entity' ∈ typeOf(e)</span>.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasGeneratedBy(gen; e,a,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">wasInformedBy(id; a2,a1,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a2)</span> AND
+<span class="name">'activity' ∈ typeOf(a1)</span>.
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name">wasStartedBy(id; a2,e,a1,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a2)</span> AND
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a1)</span>.
+
+
+
+</li><li>
+
+
+<span class="conditional">IF</span>
+ <span class="name">wasEndedBy(id; a2,e,a1,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a2)</span> AND
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a1)</span>.
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasInvalidatedBy(id; e,a,t,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(id; e2, e1, a, g2, u1, attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+ In this constraint, <span class="name">a</span>, <span class="name">g2</span>, and <span class="name">u1</span> <em class="rfc2119" title="must not">must not</em> be placeholders.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(id; e2, e1, -, -, -, attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span>.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasAttributedTo(id; e,ag,attr)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e)</span> AND
+<span class="name">'agent' ∈ typeOf(ag)</span>.
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasAssociatedWith(id; a,ag,pl,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span> AND
+<span class="name">'agent' ∈ typeOf(ag)</span> AND
+<span class="name">'entity' ∈ typeOf(pl)</span>. In this
+constraint, <span class="name">pl</span> <em class="rfc2119" title="must not">must not</em> be a placeholder.
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">wasAssociatedWith(id; a,ag,-,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'activity' ∈ typeOf(a)</span> AND
+<span class="name">'agent' ∈ typeOf(ag)</span>.
+
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">actedOnBehalfOf(id; ag2,ag1,a,attrs)</span>
+<span class="conditional">THEN</span>
+<span class="name">'agent' ∈ typeOf(ag2)</span> AND
+<span class="name">'agent' ∈ typeOf(ag1)</span> AND
+<span class="name">'activity' ∈ typeOf(a)</span>.
+
+
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">alternateOf(e2, e1)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span>.
+
+
+</li><li>
+<span class="conditional">IF</span>
+ <span class="name">specializationOf(e2, e1)</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(e2)</span> AND
+<span class="name">'entity' ∈ typeOf(e1)</span>.
+
+
+
+
+
+
+
+</li><li>
+
+
+<span class="conditional">IF</span>
+ <span class="name"><span class="delete">mentionOf(e2,e1,b)</span><span class="insert">hadMember(c,e)</span></span>
+<span class="conditional">THEN</span>
+<span class="name"><span class="insert">'prov:Collection' ∈ typeOf(c)</span></span><span class="insert"> AND
+</span><span class="name">'entity' ∈ <span class="delete">typeOf(e2)</span><span class="insert">typeOf(c)</span></span> AND
+<span class="name">'entity' ∈ <span class="delete">typeOf(e1)</span><span class="delete"> AND
+</span><span class="delete">'entity' ∈ typeOf(b)</span><span class="insert">typeOf(e)</span></span>.
+
+
+</li><li>
+
+<span class="conditional">IF</span>
+ <span class="name"><span class="delete">hadMember(c,e)</span>
+<span class="delete">THEN</span>
+<span class="delete">'prov:Collection' ∈ typeOf(c)</span><span class="delete"> AND
+</span><span class="delete">'entity' ∈ typeOf(c)</span><span class="delete"> AND
+</span><span class="delete">'entity' ∈ typeOf(e)</span><span class="delete">.
+
+
+</span>
+
+<span class="delete">IF</span>
+ entity(c,[prov:type='prov:EmptyCollection'])</span>
+<span class="conditional">THEN</span>
+<span class="name">'entity' ∈ typeOf(c)</span> AND
+<span class="name">'prov:Collection' ∈ typeOf(c)</span>AND
+<span class="name">'prov:EmptyCollection' ∈ typeOf(c)</span>.
+
+</li></ol>
+</div>
+
+</section>
+
+<section id="impossibility-constraints">
+<h3><span class="secno"><span class="delete">5.4</span><span class="insert">6.4</span> </span>Impossibility constraints</h3>
+
+<p> Impossibility constraints require that certain patterns of
+statements never appear in <a href="#dfn-valid" class="internalDFN">valid</a> PROV instances. Impossibility
+constraints have the following general form:
+</p>
+
+<div class="constraint-example" id="impossible-example"><div class="ruleTitle"><a class="internalDFN" href="#impossible-example">Constraint-example NNN (impossible-example)</a></div>
+ <p><span class="conditional">IF</span> <span class="name">hyp<sub>1</sub></span> and ... and <span class="name">hyp<sub>n</sub></span> <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+
+<p> Checking an impossibility constraint on instance <span class="math">I</span> means checking whether there is
+any way of matching the pattern <span class="name">hyp<sub>1</sub></span>, ..., <span class="name">hyp<sub>n</sub></span>. If there
+is, then checking the constraint on <span class="math">I</span> fails (which implies that
+<span class="math">I</span> is invalid).
+
+
+</p><hr>
+
+<p id="impossible-unspecified-derivation-generation-use_text">
+A derivation with unspecified activity <span class="name">wasDerivedFrom(id;e1,e2,-,g,u,attrs)</span> represents a derivation that
+ takes one or more steps, whose activity, generation and use events
+ are unspecified. It is forbidden to specify a generation or use
+ event without specifying the activity.</p>
+
+ <div class="constraint" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a class="internalDFN" href="#impossible-unspecified-derivation-generation-use">Constraint <span class="delete">53</span><span class="insert">51</span> (impossible-unspecified-derivation-generation-use)</a></div>
+<p> In the following rules, <span class="name">g</span> and <span class="name">u</span> <em class="rfc2119" title="must not">must not</em> be <span class="name">-</span>.</p>
+ <ol>
+ <li> <span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(_id;_e2,_e1,-,g,-,attrs)</span>
+ <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</li> <li> <span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(_id;_e2,_e1,-,-,u,attrs)</span>
+ <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</li>
+ <li> <span class="conditional">IF</span>
+ <span class="name">wasDerivedFrom(_id;_e2,_e1,-,g,u,attrs)</span>
+ <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</li>
+ </ol>
+ </div>
+<hr>
+
+<p id="impossible-specialization-reflexive_text">As noted previously, specialization is a
+ <a href="#dfn-strict-partial-order" class="internalDFN">strict partial order</a>: it is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>.</p>
+
+ <div class="constraint" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint <span class="delete">54</span><span class="insert">52</span> (impossible-specialization-reflexive)</a></div>
+
+ <p> <span class="conditional">IF</span> <span class="name">specializationOf(e,e)</span> <span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+
+
+
+
+
+ <hr>
+
+
+ <p id="impossible-property-overlap_text"> Furthermore, identifiers
+ of basic relationships are disjoint.
+ </p>
+ <div class="constraint" id="impossible-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-property-overlap">Constraint <span class="delete">55</span><span class="insert">53</span> (impossible-property-overlap)</a></div>
+ <p>
+For each <span class="name">r</span> and <span class="name">s</span>
+ in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>} such that <span class="name">r</span> and <span class="name">s</span>
+ are different relation names, the
+ following constraint holds:
+</p>
+ <p>
+ <span class="conditional">IF</span> <span class="name">r(id; a<sub>1</sub>,...,a<sub>m</sub>)</span> and <span class="name">s(id; b<sub>1</sub>,...,b<sub>n</sub>)</span> <span class="conditional">THEN INVALID</span>.
+ </p>
+ </div>
+
+ <div class="remark">
+ <p>Since <span class="name">wasInfluencedBy</span> is a superproperty of many other
+ properties, it is excluded from the set of properties whose
+ identifiers are required to be pairwise disjoint. The following
+ example illustrates this observation:
+ </p><pre>wasInfluencedBy(id;e2,e1)
+wasDerivedFrom(id;e2,e1)
+</pre>
+<p> This satisfies the disjointness constraint.
+ </p>
+ <p>There is, however, no
+ constraint requiring that every influence relationship is
+ accompanied by a more specific relationship having the same
+ identifier. The following valid example illustrates this observation:
+ </p><pre>wasInfluencedBy(id; e2,e1)
+</pre>
+<p> This is valid; there is no inferrable information about what kind
+ of influence relates <span class="name">e2</span> and <span class="name">e1</span>, other than its identity.
+ </p>
+ </div>
+
+ <p id="impossible-object-property-overlap_text"> Identifiers of entities,
+ agents and activities cannot also be identifiers of properties.
+ </p>
+ <div class="constraint" id="impossible-object-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-object-property-overlap">Constraint <span class="delete">56</span><span class="insert">54</span> (impossible-object-property-overlap)</a></div>
+ <p>
+For each <span class="name">p</span> in {<span class="name">entity</span>, <span class="name">activity</span>
+ or <span class="name">agent</span>} and for each <span class="name">r</span> in {
+<span class="name">used</span>,
+<span class="name">wasGeneratedBy</span>,
+<span class="name">wasInvalidatedBy</span>,
+<span class="name">wasInfluencedBy</span>,
+<span class="name">wasStartedBy</span>,
+<span class="name">wasEndedBy</span>,
+<span class="name">wasInformedBy</span>,
+<span class="name">wasDerivedFrom</span>,
+<span class="name">wasAttributedTo</span>,
+<span class="name">wasAssociatedWith</span>,
+<span class="name">actedOnBehalfOf</span>}, the following
+ impossibility constraint holds:</p>
+
+<p> <span class="conditional">IF</span> <span class="name">p(id,a<sub>1</sub>,...,a<sub>n</sub>)</span> and
+ <span class="name">r(id; b<sub>1</sub>,...,b<sub>n</sub>)</span> <span class="conditional">THEN INVALID</span>.
+ </p>
+ </div>
+
+
+
+
+ <hr>
+ <p id="entity-activity-disjoint_text"> The set of entities and activities are disjoint, expressed by
+ the following constraint:
+ </p>
+ <div class="constraint" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint <span class="delete">57</span><span class="insert">55</span> (entity-activity-disjoint)</a></div>
+
+
+<p>
+ <span class="conditional">IF</span>
+<span class="name">'entity' ∈ typeOf(id)</span> AND
+<span class="name">'activity' ∈ typeOf(id)</span>
+<span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+ <div class="remark">
+ There is no disjointness between entities and agents. This is because one might want to make statements about the provenance of an agent, by making it an entity.
+ For example, one can assert both <span class="name">entity(a1)</span> and <span class="name">agent(a1)</span> in a valid PROV instance.
+ Similarly, there is no disjointness between activities and
+ agents, and one can assert both <span class="name">activity(a1)</span> and <span class="name">agent(a1)</span> in a valid PROV instance.
+ However, one should keep in mind that some specific types of agents may not be suitable as activities.
+ For example, asserting statements such as <span class="name">agent(Bob, [type=prov:Person])</span> and <span class="name">activity(Bob)</span> is discouraged. In these cases, disjointness can be ensured by explicitly asserting the agent as both agent and entity, and applying <a class="rule-ref" href="#entity-activity-disjoint"><span>Constraint <span class="delete">57</span><span class="insert">55</span> (entity-activity-disjoint)</span></a>.
+ </div>
+
+
+ <hr>
+ <p id="membership-empty-collection_text"> An empty collection cannot contain any member, expressed by
+ the following constraint:
+ </p>
+ <div class="constraint" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint <span class="delete">58</span><span class="insert">56</span> (membership-empty-collection)</a></div>
+<p> <span class="conditional">IF</span>
+ <span class="name">hasMember(c,e)</span> and
+<span class="name">'prov:EmptyCollection' ∈ typeOf(c)</span>
+<span class="conditional">THEN</span> <span class="conditional">INVALID</span>.</p>
+ </div>
+
+
+
+</section>
+
+
+</section>
+
+ <section id="normalization-validity-equivalence">
+<h2><span class="secno"><span class="delete">6.</span><span class="insert">7.</span> </span>Normalization, Validity, and Equivalence</h2>
+
+
+ <p>We define the notions of <a title="normal form" href="#dfn-normal-form" class="internalDFN">normalization</a>, <a title="valid" href="#dfn-valid" class="internalDFN">validity</a> and
+<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"><span class="delete">6.1</span><span class="insert">7.1</span> </span>Instances</h3>
+
+<div class="remark">
+ <span class="delete">Implementations</span><span class="insert">Before normalization or validation, implementations</span> should <span class="delete">decide up front what</span><span class="insert">expand
+ namespace prefixes and perform any appropriate</span> reasoning about
+ co-reference <span class="delete">should be applied,</span><span class="insert">of identifiers,</span> 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 class="name">owl:sameAs</span> as a result of OWL
+ reasoning).
+ </div>
+
+<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 <span class="delete">constraints.</span><span class="insert">constraints, obtained as follows:</span></p>
+
+
+
+ <ol>
+ <li>
+ Apply all definitions to <span class="math">I</span> by replacing each defined statement by its
+ definition (possibly introducing fresh existential variables in
+ the process), yielding an instance <span class="math">I<sub>1</sub></span>.
+ </li>
+ <li>
+ Apply all inferences to <span class="math">I<sub>1</sub></span> by adding the conclusion of each inference
+ whose hypotheses are satisfied and whose entire conclusion does not
+ already hold (again, possibly introducing fresh existential
+ variables), yielding an instance <span class="math">I<sub>2</sub></span>.
+ </li>
+ <li>
+ Apply all uniqueness constraints to <span class="math">I<sub>2</sub></span> by <span class="insert">unifying terms or </span>merging<span class="delete"> terms or</span> statements
+ and applying the resulting substitution to the instance, yielding
+ an instance <span class="math">I<sub>3</sub></span>. If some uniqueness constraint cannot be
+ applied, then normalization fails.
+ </li>
+ <li>If no definitions, inferences, or uniqueness constraints can be applied to instance <span class="math">I<sub>3</sub></span>, then <span class="math">I<sub>3</sub></span> is the
+ normal form of <span class="math">I</span>.</li>
+ <li>Otherwise, the normal form of <span class="math">I</span> is the same as the normal form
+ of <span class="math">I<sub>3</sub></span> (that is, proceed by<span class="delete"> recursively </span>
+ normalizing <span class="math">I<sub>3</sub></span><span class="delete">).</span><span class="insert"> at step 1).</span>
+ </li></ol>
+
+<p>Because of the potential interaction among definitions, inferences, and
+ constraints, the above algorithm is <span class="delete">recursive.</span><span class="insert">iterative.</span> Nevertheless,
+ all of our constraints fall into a class of <a>tuple-generating
+ dependencies</a> and <a>equality-generating dependencies</a> that
+ satisfy a termination condition called <a>weak acyclicity</a> that
+ has been studied in the context of relational databases
+ [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>]. Therefore, the above algorithm terminates, independently
+ of the order in which inferences and constraints are applied.
+ <a href="#termination">Appendix <span class="delete">C</span><span class="insert">A</span></a> gives a proof that normalization terminates and produces
+ a unique (up to isomorphism) normal form.
+</p>
+
+ <p>
+ A PROV instance is <dfn id="dfn-valid">valid</dfn>
+if its normal form exists and <span class="delete">satisfies </span>all of
+ the validity <span class="delete">constraints; this implies that the instance satisfies
+ all of the definitions, inferences, and constraints.
+ </span><span class="insert">constraints succeed on the normal form.
+ </span>The following algorithm can be used to test
+ validity:</p>
+
+<ol>
+ <li>Normalize the instance <span class="math">I</span>, obtaining<span class="delete"> normalized instance</span><span class="insert">
+ normal form</span> <span class="math">I'</span>. If
+ normalization fails, then <span class="math">I</span> is not <a href="#dfn-valid" class="internalDFN">valid</a>.
+ </li>
+ <li>Apply all event ordering constraints to <span class="math">I'</span> to build a graph <span class="math">G</span> whose nodes
+ are event identifiers and edges
+ are labeled by "precedes"
+ and "strictly precedes" relationships among events induced by the constraints.</li>
+ <li> Determine whether there is a cycle in <span class="math">G</span> that contains a
+ "strictly precedes" edge. If so, then <span class="math">I</span> is not <a href="#dfn-valid" class="internalDFN">valid</a>.
+ </li>
+ <li>Apply the type constraints <a href="#type-constraints">(section
+ 5.3)</a> to determine whether there are any violations of
+ disjointness. If so, then <span class="math">I</span> is not <a href="#dfn-valid" class="internalDFN">valid</a>.
+ </li><li>
+ Check that none of the impossibility constraints <a href="#impossibility-constraints">(section 5.4)</a> are
+ violated. If any are violated, then <span class="math">I</span> is
+ not <a href="#dfn-valid" class="internalDFN">valid</a>. Otherwise, <span class="math">I</span> is <a href="#dfn-valid" class="internalDFN">valid</a><span class="insert">.</span>
+ </li>
+ </ol>
+
+<p>A normal form of a PROV instance does not exist when a uniqueness
+ constraint fails due to <span class="insert">unification or </span>merging failure. </p>
+
+
+
+
+
+
+<p> Two <a href="#dfn-valid" class="internalDFN"><span class="insert">valid</span></a> PROV instances are <dfn id="dfn-equivalent">equivalent</dfn> if they
+ have <a href="#dfn-isomorphic" class="internalDFN">isomorphic</a> normal <span class="delete">forms (that</span><span class="insert">forms. That</span> is, after applying all possible inference
+rules, the two instances produce the same set of PROV statements,
+up to reordering of statements and attributes within attribute lists,
+ and renaming of existential <span class="delete">variables).
+</span><span class="insert">variables.
+</span></p>
+ <p>Equivalence <span class="insert">can also be checked over pairs of PROV instances that
+ are not necessarily valid, subject to the following rules:
+ </span></p><ul>
+ <li><span class="insert">If both are valid, then equivalence is
+ defined above.</span></li>
+ <li><span class="insert">If both are invalid, then equivalence can be
+ implemented in any way provided it is </span><a href="#dfn-reflexive" class="internalDFN"><span class="insert">reflexive</span></a><span class="insert">, </span><a href="#dfn-symmetric" class="internalDFN"><span class="insert">symmetric</span></a><span class="insert">, and </span><a href="#dfn-transitive" class="internalDFN"><span class="insert">transitive</span></a><span class="insert">.
+ </span></li>
+ <li><span class="insert">If one instance is valid and the other is invalid, then the two
+ instances are not equivalent.</span></li>
+ </ul>
+ <p><span class="insert">
+Equivalence </span>has the following <span class="delete">characteristics:</span><span class="insert">characteristics over valid instances:</span> </p>
+
+<ul>
+ <li>
+ The order of provenance statements is irrelevant to the meaning of
+ a PROV instance. That is, a
+ PROV instance is equivalent to any other instance obtained by
+reordering its statements.
+ </li>
+ <li>The order of attribute-value pairs in attribute lists is
+ irrelevant to the meaning of a PROV statement. That is, a PROV
+ statement carrying attributes is equivalent to any other statement
+ obtained by reordering attribute-value pairs and eliminating
+ duplicate pairs.
+ </li>
+ <li>The particular choices of names of existential variables are irrelevant to the meaning
+ of an instance; that is, the names can be renamed without changing
+ the meaning, as long as different names are always replaced with
+ different names. (Replacing two different names with equal names,
+ however, can
+ change the meaning, so does not preserve equivalence.)</li>
+ <li>
+ Applying inference rules, definitions, and uniqueness constraints preserves equivalence. That is, a <a href="#instance" class="internalDFN">PROV
+ instance</a> is equivalent to the instance obtained by applying any
+ inference rule or definition, or by <a title="unification"><span class="insert">unifying</span></a><span class="insert"> two terms or</span> <a href="#dfn-merging" class="internalDFN">merging</a> two statements to
+ enforce a uniqueness constraint.
+ </li>
+ <li>Equivalence is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-symmetric" class="internalDFN">symmetric</a>, and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>.<span class="insert"> (This is because a valid instance has a unique
+ normal form up to isomorphism [</span><cite><a class="bibref" href="#bib-DBCONSTRAINTS"><span class="insert">DBCONSTRAINTS</span></a></cite><span class="insert">]). </span></li>
+</ul>
+
+<p> An application that processes PROV data <em class="rfc2119" title="should">should</em> handle
+equivalent instances in the same way.<span class="delete"> (Common</span><span class="insert"> This guideline is necessarily
+imprecise because "in the same way" is application-specific.
+Common</span> exceptions to this <span class="delete">rule</span><span class="insert">guideline</span>
+include, for example, <span class="delete">pretty-printers</span><span class="insert">applications</span> that <span class="delete">seek to preserve the
+original</span><span class="insert">pretty-print or digitally sign
+provenance, where the</span> order <span class="insert">and syntactic form </span>of statements <span class="delete">in a file and avoid expanding
+inferences.)</span><span class="insert">matters.</span> </p>
+
+</section>
+
+<section id="bundle-constraints">
+<h3><span class="secno"><span class="delete">6.2</span><span class="insert">7.2</span> </span>Bundles and Documents</h3>
+
+
+<p>The definitions, inferences, and constraints, and
+the resulting notions of normalization, validity and equivalence,
+<span class="delete">assume</span><span class="insert">work on</span> a <span class="insert">single </span>PROV <span class="delete">document that consists only of a </span><span class="delete">toplevel
+instance</span><span class="delete">, containing all PROV statements in the top level of the
+document (that is, not enclosed in a named </span><span class="delete">bundle</span><span class="delete">).</span><span class="insert">instance.</span> In this
+section, we describe how to deal with general PROV
+documents, possibly including multiple named <span class="delete">bundles.</span><span class="insert">bundles as well as a
+toplevel instance.</span> Briefly, each bundle is
+handled independently; there is no interaction between bundles from
+the perspective of applying definitions, inferences, or constraints,
+computing normal forms, or checking validity or equivalence.</p>
+
+<p> We model a general PROV document, containing <span class="name">n</span> named bundles
+<span class="name">b<sub>1</sub>...b<sub>n</sub></span>, as a tuple
+<span class="name"><span class="delete">(B</span><span class="insert">(I</span><sub>0</sub>,[b<sub>1</sub><span class="delete">=B</span><span class="insert">=I</span><sub>1</sub>,...,b<sub>n</sub><span class="delete">=B</span><span class="insert">=I</span><sub>n</sub>])</span>
+where <span class="name"><span class="delete">B</span><span class="insert">I</span><sub>0</sub></span> is the <span class="delete">set of
+statements of the </span>toplevel<span class="delete"> instance</span><span class="insert">
+instance, and for each </span><span class="name"><span class="insert">i</span></span>, <span class="delete">and for each </span><span class="delete">i</span><span class="delete">, </span><span class="delete">B</span><span class="name"><span class="insert">I</span><sub>i</sub></span> is the <span class="delete">set of
+statements of </span><span class="insert">instance associated with
+</span>bundle <span class="name">b<sub>i</sub></span>.<span class="delete"> Names </span><span class="delete">b</span><span class="delete">1</span><span class="delete">...b</span><span class="delete">n</span><span class="delete"> are assumed to be distinct. </span> This notation is shorthand for the
+following PROV-N syntax:</p>
+
+<div class="name">
+<span class="delete">B</span><span class="insert">document</span><br><span class="insert">
+ I</span><sub>0</sub><br>
+<span class="delete">bundle</span><span class="insert"> bundle</span> b<sub>1</sub><br>
+<span class="delete"> B</span><span class="insert"> I</span><sub>1</sub><br>
+<span class="delete">endBundle</span><span class="insert"> endBundle</span><br>
+<span class="delete">...</span><span class="insert"> ...</span><br>
+<span class="delete">bundle</span><span class="insert"> bundle</span> b<sub>n</sub><br>
+<span class="delete"> B</span><span class="insert"> I</span><sub>n</sub><br>
+<span class="delete">endBundle</span><span class="insert"> endBundle</span><br><span class="insert">
+endDocument</span>
+</div>
+
+
+
+
+<p> The <a href="#dfn-normal-form" class="internalDFN">normal form</a> of a PROV document
+<span class="name"><span class="delete">(B</span><span class="insert">(I</span><sub>0</sub>,[b<sub>1</sub><span class="delete">=B</span><span class="insert">=I</span><sub>1</sub>,...,[b<sub>n</sub><span class="delete">=B</span><span class="insert">=I</span><sub>n</sub>])</span> is <span class="name"><span class="delete">(B'</span><span class="insert">(I'</span><sub>0</sub>,[b<sub>1</sub><span class="delete">=B'</span><span class="insert">=I'</span><sub>1</sub>,...,b<sub>n</sub><span class="delete">=B'</span><span class="insert">=I'</span><sub>n</sub>])</span>
+where <span class="name"><span class="delete">B'</span><span class="insert">I'</span><sub>i</sub></span> is the normal
+form of <span class="name"><span class="delete">B</span><span class="insert">I</span><sub>i</sub></span> for each <span class="name">i</span> between 0 and <span class="name">n</span>. </p>
+
+<p>A PROV document is <a href="#dfn-valid" class="internalDFN">valid</a> if each of the bundles <span class="name"><span class="delete">B</span><span class="insert">I</span><sub>0</sub></span>,
+..., <span class="name"><span class="delete">B</span><span class="insert">I</span><sub>n</sub></span> are valid and none of the bundle identifiers <span class="name">b<sub>i</sub></span> are repeated.</p>
+
+<p>Two (valid) PROV documents <span class="name"><span class="delete">(B</span><span class="insert">(I</span><sub>0</sub>,[b<sub>1</sub><span class="delete">=B</span><span class="insert">=I</span><sub>1</sub>,...,b<sub>n</sub><span class="delete">=B</span><span class="insert">=I</span><sub>n</sub>])</span> and
+<span class="name"><span class="delete">(B'</span><span class="insert">(I'</span><sub>0</sub>,[b<sub>1</sub><span class="delete">'=B'</span><span class="insert">'=I'</span><sub>1</sub>,...,b'<sub>m</sub><span class="delete">=B'</span><span class="insert">=I'</span><sub>m</sub>])</span> are <a href="#dfn-equivalent" class="internalDFN">equivalent</a> if <span class="name"><span class="delete">B</span><span class="insert">I</span><sub>0</sub></span> is
+equivalent to <span class="name"><span class="delete">B'</span><span class="insert">I'</span><sub>0</sub></span> and <span class="name">n = m</span> and
+there exists a permutation <span class="name">P : {1..n} -> {1..n}</span> such that for each <span class="name">i</span>, <span class="name">b<sub>i</sub> =
+b'<sub>P(i)</sub></span> and <span class="name"><span class="delete">B</span><span class="insert">I</span><sub>i</sub></span> is equivalent to <span class="name"><span class="delete">B'</span><span class="insert">I'</span><sub>P(i)</sub></span>.
+</p>
+
+</section>
+
+
+</section>
+
+
+
+
+
+
+
+
+
+
+
+<section class="glossary" id="glossary">
+ <h2><span class="secno"><span class="delete">7.</span><span class="insert">8.</span> </span>Glossary</h2>
+
+ <ul>
+ <li> <dfn id="dfn-antisymmetric">antisymmetric</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-antisymmetric" class="internalDFN">antisymmetric</a> if
+ for any elements <span class="math">x</span>, <span class="math">y</span> of <span class="math">X</span>, if <span class="math">x R y</span> and <span class="math">y R x</span> then <span class="math">x = y</span>.</li>
+ <li> <dfn id="dfn-asymmetric">asymmetric</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-asymmetric" class="internalDFN">asymmetric</a> if
+ <span class="math">x R y</span> and <span class="math">y R x</span> do not hold for any elements <span class="math">x</span>, <span class="math">y</span> of <span class="math">X</span>.</li>
+ <li><dfn id="dfn-equivalence-relation">equivalence relation</dfn>: An equivalence relation is a relation
+ that is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-symmetric" class="internalDFN">symmetric</a>, and
+ <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li> <dfn id="dfn-irreflexive">irreflexive</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> if
+ for <span class="math">x R x</span> does not hold for any element <span class="math">x</span> of <span class="math">X</span>.</li>
+ <span class="delete">reflexive</span><span class="delete">: A relation </span><span class="delete">R</span><span class="delete"> over </span><span class="delete">X</span><span class="delete"> is </span><span class="delete">reflexive</span><span class="delete"> if
+ for any element </span><span class="delete">x</span><span class="delete"> of </span><span class="delete">X</span><span class="delete">, we have </span><span class="delete">x R x</span><span class="delete">.</span>
+
+ <li><dfn id="dfn-partial-order">partial order</dfn>: A partial order is a relation
+ that is <a href="#dfn-reflexive" class="internalDFN">reflexive</a>, <a href="#dfn-antisymmetric" class="internalDFN">antisymmetric</a>, and <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li><dfn id="dfn-preorder">preorder</dfn>: A preorder is a relation that is
+ <a href="#dfn-reflexive" class="internalDFN">reflexive</a> and <a href="#dfn-transitive" class="internalDFN">transitive</a>. (It is not necessarily antisymmetric,
+ meaning there can be cycles of distinct elements <span class="math">x<sub>1</sub> R x<sub>2</sub> R ... R
+ x<sub>n</sub> R x<sub>1</sub>.</span></li>
+ <li> <dfn id="dfn-reflexive"><span class="insert">reflexive</span></dfn><span class="insert">: A relation </span><span class="math"><span class="insert">R</span></span><span class="insert"> over </span><span class="math"><span class="insert">X</span></span><span class="insert"> is </span><a href="#dfn-reflexive" class="internalDFN"><span class="insert">reflexive</span></a><span class="insert"> if
+ for any element </span><span class="math"><span class="insert">x</span></span><span class="insert"> of </span><span class="math"><span class="insert">X</span></span><span class="insert">, we have </span><span class="math"><span class="insert">x R x</span></span><span class="insert">.</span></li>
+ <li><dfn id="dfn-strict-partial-order">strict partial order</dfn>: A strict partial order is a
+ relation that is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a>, <a href="#dfn-asymmetric" class="internalDFN">asymmetric</a> and <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li><dfn id="dfn-strict-preorder">strict preorder</dfn>: A strict preorder is a relation
+ that is <a href="#dfn-irreflexive" class="internalDFN">irreflexive</a> and <a href="#dfn-transitive" class="internalDFN">transitive</a>.</li>
+ <li> <dfn id="dfn-symmetric">symmetric</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-symmetric" class="internalDFN">symmetric</a> if
+ for any elements <span class="math">x</span>, <span class="math">y</span> of <span class="math">X</span>, if <span class="math">x R y</span> then <span class="math">y R x</span>.</li>
+ <li> <dfn id="dfn-transitive">transitive</dfn>: A relation <span class="math">R</span> over <span class="math">X</span> is <a href="#dfn-transitive" class="internalDFN">transitive</a> if
+ for any elements <span class="math">x</span>, <span class="math">y</span>, <span class="math">z</span> of <span class="math">X</span>, if <span class="math">x R y</span> and <span class="math">y R z</span> then <span class="math">x R z</span>.</li>
+
+
+ </ul>
+ </section>
+
+
+ <section class="appendix informative" id="termination">
+ <h2><span class="secno">A. </span>Termination of normalization</h2><p><em>This section is non-normative.</em></p>
+
+ <p>
+ We will show that normalization terminates, that is, that
+ applying definitions, inferences and uniqueness/key constraints
+ eventually either fails (due to constraint violation) or
+ terminates with a normal form.
+ </p>
+ <p>
+ First, since the inferences and constraints never introduce new
+ defined statements, for the purpose of termination we always expand
+ the definitions first and then consider only normalization of
+ instances in which there are no remaining defined statements.
+ </p>
+ <p>We will prove termination for the simple case where there are no
+ attributes. For the general case, we will show that any
+ nontermination arising from an instance that does involve
+ 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
+ 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
+ in a modular fashion for our system, because there are only a few possible
+ cycles among statements. The following table summarizes seven
+ <em>stages</em> of the inference rules; because there are no
+ cycles among stages, it is sufficient to check weak acyclicity
+ of each stage independently.
+ </p>
+
+ <table border="1">
+ <tbody><tr>
+ <th>Stage #</th>
+ <th>Inference</th>
+ <th>Hypotheses</th>
+ <th>Conclusions</th>
+ </tr>
+ <tr>
+ <td>1</td>
+ <td>19, 20, <span class="delete">21, 22</span><span class="insert">21</span></td>
+ <td class="name"><span class="delete">specializationOf, mentionOf</span><span class="insert">specializationOf</span></td>
+
+ <td class="name">specializationOf, entity</td>
+ </tr>
+ <tr>
+ <td>2</td>
+ <td>7, 8, 13, 14</td>
+ <td class="name">entity, activity, wasAttributedTo, actedOnBehalfOf</td>
+ <td class="name">wasInvalidatedBy, wasStartedBy, <span class="delete">wasEndedBy</span><span class="insert">wasEndedBy,
+ wasAssociatedWith</span></td>
+ </tr>
+ <tr>
+ <td>3</td>
+ <td>9, 10</td>
+ <td class="name">wasStartedBy, wasEndedBy</td>
+ <td class="name">wasGeneratedBy</td>
+ </tr>
+ <tr>
+ <td>4</td>
+ <td>11, 12</td>
+ <td class="name">wasDerivedFrom</td>
+ <td class="name">wasGeneratedBy, used, alternateOf</td>
+ </tr>
+ <tr>
+ <td>5</td>
+ <td>16, 17, 18</td>
+ <td class="name">alternateOf, entity</td>
+ <td class="name">alternateOf</td>
+ </tr>
+ <tr>
+ <td>6</td>
+ <td>5, 6</td>
+ <td class="name">wasInformedBy, generated, used</td>
+ <td class="name">wasInformedBy, generated, used</td>
+ </tr>
+ <tr>
+ <td>7</td>
+ <td>15</td>
+ <td>many</td>
+ <td class="name">wasInfluencedBy</td>
+ </tr>
+
+ </tbody></table>
+ <p>
+ For each stage, we show that the stage is weakly acyclic.
+ </p><ul><li>Stages 1 and 5 have no rules with existential quantifiers,
+ so they are weakly acyclic.
+ </li>
+ <li>Stages 2, 3, 4, and 7 have no cycles among the formulas
+ involved, so they are weakly acyclic.
+ </li>
+ <li>For stage 6, we check weak acyclicity using the algorithm
+ in [<cite><a class="bibref" href="#bib-DBCONSTRAINTS">DBCONSTRAINTS</a></cite>], namely:
+ <ul><li> Given a formula <span class="math">φ(x<sub>1</sub>,...,x<sub>n</sub>) ⇒
+ ∃y<sub>1</sub>,...,y<sub>m</sub>. ψ(x<sub>1</sub>,...,x<sub>n</sub>,y<sub>1</sub>,...,y<sub>m</sub>)</span></li>
+ <li>For every <span class="math">x</span> that occurs in <span class="math">ψ</span>, and for every
+ occurrence of <span class="math">x</span> in <span class="math">φ</span> in position <span class="math">r.i</span>:
+ <ol><li>For every occurrence of <span class="math">x</span> in position <span class="math">s.j</span>, add
+ an edge from <span class="math">r.i</span> to <span class="math">s.j</span> (if it does
+ not already exist). </li>
+ <li>In addition, for every existentially quantified variable <span class="math">y</span>
+ and for every occurrence of <span class="math">y</span> in <span class="math">ψ</span> in position
+ <span class="math">t.k</span>, add a special edge from <span class="math">r.i</span> to <span class="math">t.k</span> (if it does
+ not already exist).
+ </li>
+ </ol>
+ </li>
+ </ul>
+ Weak
+ acyclicity means that there is no cycle involving a special
+ edge in the resulting graph. For the two inferences in stage 6,
+ the following dependency graph witnesses weak
+ acyclicity. The nodes <span class="name">wasGeneratedBy.i</span>,
+ <span class="name">wasInformedBy.i</span>, and <span class="name">used.i</span> denote the <span class="math">i</span>th arguments
+ of the corresponding predicates. The solid edges are ordinary
+ edges, and the dashed edges are <em>special</em> edges.
+ </li>
+ </ul>
+
+
+ <img src="images/constraints/weak-acyclic-6.svg" alt="Graph illustrating weak
+ acyclicity of stage 6">
+
+ <p><b>Termination for instances with attributes.</b>
+ We can translate an instance with attributes to an alternative,
+ purely relational language by introducing a relation
+ <span class="name">attribute(id,a,v)</span> and replacing every statement of the form
+ <span class="name">r(id;a1,...,a<sub>n</sub>,[(k<sub>1</sub>,v<sub>1</sub>),...,(k<sub>m</sub>,v<sub>m</sub>)])</span> with
+ <span class="name">r(id;a1,...,a<sub>n</sub>),attribute(id,k<sub>1</sub>,v<sub>1</sub>),...,attribute(id,k<sub>m</sub>,v<sub>m</sub>)</span>,
+ and similarly for <span class="name">entity</span>, <span class="name">activity</span> and <span class="name">agent</span>
+ attributes. The inference rules can also be translated so as
+ to work on these instances, and a similar argument to
+ the above shows that inference is terminating on instances with
+ explicit attributes. Any infinite
+ sequence of normalization steps on the original instance would
+ lead to an infinite sequence of translated normalization steps
+ on instances with explicit attributes.
+ </p>
+</section>
+
+<section class="appendix" id="changes-since-last-version">
+ <h2><span class="secno">B. </span><span class="insert">Changes since last version</span></h2>
+ <p><span class="insert"> Please see the </span><a href="http://www.w3.org/2011/prov/wiki/ResponsesToPublicComments"><span class="insert">
+ Responses to Public Comments on the Last Call Working Draft</span></a><span class="insert">
+ for more details about the justification of these changes.</span></p>
+
+<ul>
+ <li><span class="insert">Abstract: clarified that term "validity" is analogous to other
+ notions of validity in Web standards. </span></li>
+ <li><span class="insert">Added bullet point linking to PROV-SEM under "How to read the
+ PROV family of specifications"</span></li>
+ <li><span class="insert">Revised sec. 1.2 to clarify terminology (validity), emphasize
+ that any implementation equivalent to the procedural specification
+ is compliant, and clarify that treating "equivalent instances in the
+ same way" is a guideline.</span></li>
+ <li><span class="insert">Added paragraph to sec 2.4 to clarify the purpose of the section.</span></li>
+ <li><span class="insert">Sec 2.4 Unification and Merging: changed "merging" to "unification" for terms</span></li>
+ <li><span class="insert">Sec. 2.4 "Applying definitions, inferences and constraints":
+ Updated merging to unification and added paragraph reinforcing that
+ compliance is algorithm independent</span></li>
+ <li><span class="insert">Sec. 2.4 "Checking ordering, typing and impossibility
+ constraints": Avoided use of the term "satisfies".</span></li>
+ <li><span class="insert">Sec. 2.4 "Equivalence and Isomorphism": Extended equivalence to
+ be defined on all instances, valid or not. Removed analogy to RDF.</span></li>
+ <li><span class="insert">Sec. 2.4 "From Instances to Bundles and Documents": Revised to
+ avoid giving the impression that toplevel instances must be disjoint
+ from bundles; removed reference to RDF.</span></li>
+ <li><span class="insert">Sec. 3. Clarified and reinforced algorithm independence.</span></li>
+ <li><span class="insert">Sec. 4. Added clarifying remark about role of definitions.</span></li>
+ <li><span class="insert">Sec. 4. Avoided reference to RDF, minor clarifications to
+ discussion of existential variables. </span></li>
+ <li><span class="insert">Sec. 4.1. Spelling correction.</span></li>
+ <li><span class="insert">Sec. 4.4. Merging -> unification</span></li>
+ <li><span class="insert">Sec. 5. Merging -> unification terminology change. Added
+ declarative definition of unification. Clarified
+ procedural definition. Removed definition of merging of attribute
+ lists. Updated descriptions of uniqueness and key constraint application.</span></li>
+ <li><span class="insert">Constraint 23. Renamed e, a, ag to id.</span></li>
+ <li><span class="insert">Sec. 5.2. Explicitly stated that strictly-precedes is irreflexive.</span></li>
+ <li><span class="insert">Sec. 5.2. Spelling</span></li>
+ <li><span class="insert">Sec. 5.2, just before constraint 51: updated text to accurately
+ describe constraint.</span></li>
+ <li><span class="insert">Sec. 6. Merging -> unification. Updated definition of validity
+ to avoid referring to "satisfies". Explicitly defined isomorphism
+ of instances. Broadened the definition of equivalence so that it is
+ allowed to test arbitrary instances for equivalence. Reinforce the
+ intention of the guideline that applications treat equivalent
+ instances "in the same way".</span></li>
+ <li><span class="insert">Dropped RDF as a normative reference.</span></li>
+ <li><span class="insert">Made PROV-DM and PROV-N into normative references.</span></li>
+ <li><span class="insert">Added "document" and "endDocument" to sec. 6.2.</span></li>
+ <li><span class="insert">Added sentence of explanation of purpose to beginning.</span></li>
+ <li><span class="insert">Moved "mention" to a separate note. </span></li>
+ <li><span class="insert">Added </span><a href="#concepts"><span class="insert">Section 4: Basic Concepts</span></a><span class="insert">.</span></li>
+ <li><span class="insert">Miscellaneous final cleanup prior to CR staging.</span></li>
+</ul>
+
+</section>
+
+<section class="appendix" id="acknowledgements">
+ <h2><span class="secno"><span class="insert">C.</span> </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. The editors extend special thanks to Ivan Herman (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr>), Paul Groth, Tim Lebo, Simon Miles, Stian Soiland-Reyes, for their thorough reviews.
+ </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 (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="Massachusetts Institute of Technology">MIT</abbr>),
+Jörn Hees (German Research Center for Artificial Intelligence (DFKI) Gmbh),
+Ivan Herman, (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr>),
+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>
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+</section>
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+<section id="references" class="appendix"><h2><span class="secno"><span class="delete">C.</span><span class="insert">D.</span> </span>References</h2><section id="normative-references"><h3><span class="secno"><span class="delete">C.1</span><span class="insert">D.1</span> </span>Normative references</h3><dl class="bibliography"><span class="delete">[IRI]</span><dt id="bib-PROV-DM"><span class="insert">[PROV-DM]</span></dt><dd><span class="delete">M. Duerst, M. Suignard. </span><span class="insert">Luc Moreau; Paolo Missier; eds. </span><a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/"><cite><span class="delete">Internationalized Resource Identifiers (IRI).</span><span class="insert">PROV-DM: The PROV Data Model</span></cite></a><span class="delete"> January 2005. Internet RFC 3987.</span><span class="insert">. 11 December 2012, W3C Candidate Recommendation.</span> URL: <span class="delete">http://www.ietf.org/rfc/rfc3987.txt</span>
+<a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/"><span class="insert">http://www.w3.org/TR/2012/CR-prov-dm-20121211/</span></a>
+</dd><span class="delete">[RDF]</span><dt id="bib-PROV-N"><span class="insert">[PROV-N]</span></dt><dd><span class="delete">Graham Klyne and Jeremy J. Carroll (eds.) </span><span class="insert">Luc Moreau; Paolo Missier; eds. </span><a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/"><cite><span class="delete">Resource Description Framework (RDF): Concepts and Abstract Syntax</span><span class="insert">PROV-N: The Provenance Notation</span></cite></a>. <span class="delete">2004,</span><span class="insert">11 December 2012,</span> W3C <span class="insert">Candidate </span>Recommendation. URL: <span class="delete">http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/</span><a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/"><span class="insert">http://www.w3.org/TR/2012/CR-prov-n-20121211/</span></a>
+</dd><dt id="bib-PROV-O"><span class="insert">[PROV-O]</span></dt><dd><span class="insert">Timothy Lebo; Satya Sahoo; Deborah McGuinness; eds. </span><a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/"><cite><span class="insert">Provenance Formal Model</span></cite></a><span class="insert">. 11 December 2012, W3C Candidate Recommendation. URL: </span><a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/"><span class="insert">http://www.w3.org/TR/2012/CR-prov-o-20121211/</span></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-RFC3987"><span class="insert">[RFC3987]</span></dt><dd><span class="insert">M. Dürst; M. Suignard. </span><a href="http://www.ietf.org/rfc/rfc3987.txt"><cite><span class="insert">Internationalized Resource Identifiers (IRIs).</span></cite></a><span class="insert"> January 2005. Internet RFC 3987. URL: </span><a href="http://www.ietf.org/rfc/rfc3987.txt"><span class="insert">http://www.ietf.org/rfc/rfc3987.txt</span></a>
+</dd></dl></section><section id="informative-references"><h3><span class="secno"><span class="delete">C.2</span><span class="insert">D.2</span> </span>Informative references</h3><dl class="bibliography"><dt id="bib-CHR">[CHR]</dt><dd>Thom <span class="delete">Frühwirth</span><span class="insert">Frühwirth.</span> <a href="http://constraint-handling-rules.org/"><cite>Constraint Handling Rules</cite></a>. Cambridge University Press URL: <a href="http://constraint-handling-rules.org/">http://constraint-handling-rules.org/</a>
+</dd><dt id="bib-CLOCK">[CLOCK]</dt><dd><span class="delete">Lamport, </span>L.<span class="insert"> Lamport.</span> <a href="http://research.microsoft.com/users/lamport/pubs/time-clocks.pdf"><cite>Time, clocks, and the ordering of events in a distributed system</cite></a>. Communications of the ACM 21 (7): 558–565. 1978. URL: <a href="http://research.microsoft.com/users/lamport/pubs/time-clocks.pdf">http://research.microsoft.com/users/lamport/pubs/time-clocks.pdf</a> DOI: doi:10.1145/359545.359563.
+</dd><dt id="bib-DBCONSTRAINTS">[DBCONSTRAINTS]</dt><dd> Ronald <span class="delete">Fagin,</span><span class="insert">Fagin;</span> Phokion G. <span class="delete">Kolaitis,</span><span class="insert">Kolaitis;</span> Renée J. <span class="delete">Miller, and</span><span class="insert">Miller;</span> Lucian <span class="delete">Popa</span><span class="insert">Popa.</span> <a href="http://dx.doi.org/10.1016/j.tcs.2004.10.033"><cite>Data exchange: Semantics and query answering</cite></a>. Theoretical computer science 336(1):89-124 Elsevier URL: <a href="http://dx.doi.org/10.1016/j.tcs.2004.10.033">http://dx.doi.org/10.1016/j.tcs.2004.10.033</a>
+</dd><dt id="bib-Logic">[Logic]</dt><dd>W. E. <span class="delete">Johnson</span><span class="insert">Johnson. </span><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><span class="delete">[PROV-DM]</span><dt id="bib-PROV-AQ"><span class="insert">[PROV-AQ]</span></dt><dd><span class="delete">Luc Moreau and Paolo Missier (eds.) Khalid Belhajjame, Reza B'Far, James Cheney, Stephen Cresswell, Yolanda Gil,</span><span class="insert">Graham Klyne;</span> Paul <span class="delete">Groth, Graham Klyne, Jim McCusker, Simon Miles, James Myers, Satya Sahoo, and Curt Tilmes </span><span class="insert">Groth; eds. </span><a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/"><cite><span class="delete">PROV-DM: The PROV Data Model</span><span class="insert">Provenance Access and Query</span></cite></a>. <span class="insert">19 June </span>2012, Working Draft. URL: <span class="delete">http://www.w3.org/TR/prov-dm/</span><a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/"><span class="insert">http://www.w3.org/TR/2012/WD-prov-aq-20120619/</span></a>
+</dd><span class="delete">[PROV-N]</span><dt id="bib-PROV-OVERVIEW"><span class="insert">[PROV-OVERVIEW]</span></dt><dd><span class="delete">Luc Moreau and Paolo Missier (eds.), James Cheney, Stian Soiland-Reyes </span><span class="insert">Editors TBD. </span><a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/"><cite><span class="delete">PROV-N:</span><span class="insert">PROV-OVERVIEW:</span> The <span class="delete">Provenance Notation</span><span class="insert">PROV Family of Documents</span></cite></a>. <span class="delete">2011,</span><span class="insert">11 December 2012,</span> Working Draft. URL: <span class="delete">http://www.w3.org/TR/prov-n/</span><a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/"><span class="insert">http://www.w3.org/TR/2012/WD-prov-overview-20121211/</span></a>
+</dd><span class="delete">[PROV-O]</span><dt id="bib-PROV-PRIMER"><span class="insert">[PROV-PRIMER]</span></dt><dd><span class="delete">Timothy Lebo, Satya Sahoo and Deborah McGuinness (eds.) Khalid Belhajjame, James Cheney, David Corsar, Daniel Garijo, Stian Soiland-Reyes, and Stephan Zednik </span><span class="insert">Yolanda Gil; Simon Miles; eds. </span><a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/"><cite><span class="delete">Provenance Formal</span><span class="insert">Prov</span> Model<span class="insert"> Primer</span></cite></a>. <span class="delete">2011,</span><span class="insert">11 December 2012,</span> Working Draft. URL: <span class="delete">http://www.w3.org/TR/prov-o/</span><a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/"><span class="insert">http://www.w3.org/TR/2012/WD-prov-primer-20121211/</span></a>
+</dd><dt id="bib-PROV-SEM">[PROV-SEM]</dt><dd>James <span class="delete">Cheney</span><span class="insert">Cheney; ed.</span> <a href="http://www.w3.org/2011/prov/wiki/FormalSemanticsStrawman"><cite>Formal Semantics Strawman</cite></a>. 2011, Work in progress. URL: <a href="http://www.w3.org/2011/prov/wiki/FormalSemanticsStrawman">http://www.w3.org/2011/prov/wiki/FormalSemanticsStrawman</a>
+</dd><dt id="bib-PROV-XML"><span class="insert">[PROV-XML]</span></dt><dd><span class="insert">Hook Hua; Curt Tilmes; Stephan Zednik; eds. </span><a href="http://www.w3.org/TR/2012/WD-prov-xml-20121211/"><cite><span class="insert">PROV-XML: The PROV XML Schema</span></cite></a><span class="insert">. 11 December 2012, Working Draft. URL: </span><a href="http://www.w3.org/TR/2012/WD-prov-xml-20121211/"><span class="insert">http://www.w3.org/TR/2012/WD-prov-xml-20121211/</span></a>
+</dd></dl></section></section></body></html>
+