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* initial pass responding to comments on prov-sem
authorjcheney@inf.ed.ac.uk
Fri, 01 Mar 2013 15:49:14 +0000
changeset 5807 a87e15a9aab6
parent 5806 8016c1939a67
child 5809 a770fe6f4f42
* initial pass responding to comments on prov-sem
semantics/prov-sem-math-test.html
semantics/prov-sem.html 
--- a/semantics/prov-sem-math-test.html	Thu Feb 28 17:52:30 2013 +0000
+++ b/semantics/prov-sem-math-test.html	Fri Mar 01 15:49:14 2013 +0000
@@ -768,13 +768,13 @@
 }
 
 
-</style><link rel="stylesheet" href="http://www.w3.org/StyleSheets/TR/W3C-ED"><style type="text/css">DIV.MathJax_MathML {text-align: center; margin: .75em 0px}
+</style><link rel="stylesheet" href="http://www.w3.org/StyleSheets/TR/W3C-WD"><style type="text/css">DIV.MathJax_MathML {text-align: center; margin: .75em 0px}
 .MathJax_MathML {font-style: normal; font-weight: normal; line-height: normal; font-size: 100%; font-size-adjust: none; text-indent: 0; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; border: 0; padding: 0; margin: 0}
 span.MathJax_MathML {display: inline}
 div.MathJax_MathML {display: block}
 .MathJax_mmlExBox {display: block; overflow: hidden; height: 1px; width: 60ex; padding: 0; border: 0; margin: 0}
 </style><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--></head> 
-  <body><div class="head">
+  <body><div id="MathJax_Message" style="display: none; "></div><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>
@@ -782,11 +782,11 @@
   </p>
   <h1 class="title" id="title">Semantics of the PROV Data Model</h1>
   
-  <h2 id="w3c-editor-s-draft-28-february-2013"><abbr title="World Wide Web Consortium">W3C</abbr> Editor's Draft 28 February 2013</h2>
+  <h2 id="w3c-working-draft-12-march-2013"><abbr title="World Wide Web Consortium">W3C</abbr> Working Draft 12 March 2013</h2>
   <dl>
     
       <dt>This version:</dt>
-      <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd>
+      <dd><a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">http://www.w3.org/TR/2013/WD-prov-sem-20130312/</a></dd>
       <dt>Latest published version:</dt>
       <dd><a href="http://www.w3.org/TR/prov-sem/">http://www.w3.org/TR/prov-sem/</a></dd>
     
@@ -797,8 +797,9 @@
     
     
     
-      
     
+      <dt>Previous version:</dt>
+      <dd><a href=""></a></dd>
     
     
     <dt>Editor:</dt>
@@ -826,7 +827,7 @@
     
   
   <hr>
-</div><div id="MathJax_Message" style="display: none; "></div> 
+</div> 
 
     <section id="abstract" class="introductory"><h2>Abstract</h2>
 <p>
@@ -839,11 +840,11 @@
 
 
 <p> This document presents a model-theoretic semantics for the PROV
-data model (called the <dfn id="dfn-reference-semantics">reference semantics</dfn>), viewing
+data model (called the <dfn id="dfn-naive-semantics">naive semantics</dfn>), viewing
 PROV-DM statements as atomic formulas in the sense of first-order
 logic, and viewing the constraints and inferences specified in
 PROV-CONSTRAINTS as a first-order theory. It is shown that the
-first-order theory is sound with respect to the reference semantics.
+first-order theory is sound with respect to the naive semantics.
 This information may be useful to researchers or users of PROV to
 understand the intended meaning and use of PROV for modeling
 information about the actual history, derivation or evolution of Web
@@ -851,7 +852,7 @@
 constraints or inferences for reasoning about PROV or integration of
 PROV with other Semantic Web vocabularies.  It is <b>not</b> proposed
 as a canonical or required semantics of PROV and does not place any
-constraints on use of PROV.</p>
+constraints on the use of PROV.</p>
 
 <p>The PROV Document Overview describes the overall state of PROV, and should be read before other PROV documents.</p>
 </section><section id="sotd" class="introductory"><h2>Status of This Document</h2>
@@ -874,18 +875,22 @@
 <li> <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> (Proposed Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [<cite><a class="bibref" href="#bib-PROV-O">PROV-O</a></cite>];</li>
 <li> <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> (Proposed Recommendation), the PROV data model for provenance [<cite><a class="bibref" href="#bib-PROV-DM">PROV-DM</a></cite>];</li>
 <li> <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> (Proposed Recommendation), a notation for provenance aimed at human consumption [<cite><a class="bibref" href="#bib-PROV-N">PROV-N</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> (Proposed Recommendation), a set of constraints applying to the PROV data model  (this document);</li>
+<li> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a>
+(Proposed Recommendation), a set of constraints applying to the PROV
+data model [<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>];</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> (To be published as Note),  an XML schema for the PROV data model [<cite><a class="bibref" href="#bib-PROV-XML">PROV-XML</a></cite>];</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">PROV-AQ</a> (To be published as Note), the mechanisms for accessing and querying provenance [<cite><a class="bibref" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">PROV-DICTIONARY</a> (To be published as Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>];</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> (To be published as Note) provides a mapping between PROV and Dublic Core Terms [<cite><a class="bibref" href="#bib-PROV-DC">PROV-DC</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> (To be published as Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a class="bibref" href="#bib-PROV-SEM">PROV-SEM</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a>
+(To be published as Note), a declarative specification in terms of
+first-order logic of the PROV data model (this document);</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> (To be published as Note) introduces a mechanism to link across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>].</li>
 </ul>
 
 
         <p>
-          This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as an Editor's Draft.
+          This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as a Working Draft.
           
           
           If you wish to make comments regarding this document, please send them to 
@@ -900,7 +905,7 @@
         
         
           </p><p>
-            Publication as an Editor's Draft does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
+            Publication as a Working Draft 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>
@@ -911,7 +916,7 @@
             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>.
           
-          
+          The group does not expect this document to become a <abbr title="World Wide Web Consortium">W3C</abbr> Recommendation.
           
             
               <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> 
@@ -928,7 +933,7 @@
       
     
   
-</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1. </span>Introduction</a><ul class="toc"><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.1 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.2 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.3 </span> Audience </a></li></ul></li><li class="tocline"><a href="#basics" class="tocxref"><span class="secno">2. </span> Basics </a><ul class="toc"><li class="tocline"><a href="#identifiers" class="tocxref"><span class="secno">2.1 </span> Identifiers </a></li><li class="tocline"><a href="#times-and-intervals" class="tocxref"><span class="secno">2.2 </span> Times and Intervals </a></li><li class="tocline"><a href="#attributes-and-values" class="tocxref"><span class="secno">2.3 </span> Attributes and Values </a></li><li class="tocline"><a href="#formulas" class="tocxref"><span class="secno">2.4 </span>Atomic Formulas</a></li><li class="tocline"><a href="#first-order-formulas" class="tocxref"><span class="secno">2.5 </span>First-Order Formulas</a></li></ul></li><li class="tocline"><a href="#structures" class="tocxref"><span class="secno">3. </span> Structures and Interpretations </a><ul class="toc"><li class="tocline"><a href="#things-1" class="tocxref"><span class="secno">3.1 </span> Things </a></li><li class="tocline"><a href="#objects-1" class="tocxref"><span class="secno">3.2 </span> Objects </a><ul class="toc"><li class="tocline"><a href="#entities-1" class="tocxref"><span class="secno">3.2.1 </span> Entities </a><ul class="toc"><li class="tocline"><a href="#plans-1" class="tocxref"><span class="secno">3.2.1.1 </span> Plans </a></li></ul></li><li class="tocline"><a href="#actvities" class="tocxref"><span class="secno">3.2.2 </span> Actvities </a></li><li class="tocline"><a href="#agents-1" class="tocxref"><span class="secno">3.2.3 </span> Agents </a></li><li class="tocline"><a href="#interactions-1" class="tocxref"><span class="secno">3.2.4 </span> Interactions </a><ul class="toc"><li class="tocline"><a href="#events-1" class="tocxref"><span class="secno">3.2.4.1 </span> Events </a></li><li class="tocline"><a href="#associations-1" class="tocxref"><span class="secno">3.2.4.2 </span> Associations </a></li><li class="tocline"><a href="#communications" class="tocxref"><span class="secno">3.2.4.3 </span>Communications</a></li><li class="tocline"><a href="#delegations" class="tocxref"><span class="secno">3.2.4.4 </span>Delegations</a></li><li class="tocline"><a href="#derivations-1" class="tocxref"><span class="secno">3.2.4.5 </span> Derivations </a></li></ul></li></ul></li><li class="tocline"><a href="#relations" class="tocxref"><span class="secno">3.3 </span> Relations </a><ul class="toc"><li class="tocline"><a href="#derivation-paths-and-derivedfrom" class="tocxref"><span class="secno">3.3.1 </span> Derivation paths and DerivedFrom </a></li></ul></li><li class="tocline"><a href="#putting-it-all-together" class="tocxref"><span class="secno">3.4 </span> Putting it all together </a></li><li class="tocline"><a href="#interpretations" class="tocxref"><span class="secno">3.5 </span> Interpretations </a></li></ul></li><li class="tocline"><a href="#semantics" class="tocxref"><span class="secno">4. </span> Semantics </a><ul class="toc"><li class="tocline"><a href="#satisfaction" class="tocxref"><span class="secno">4.1 </span> Satisfaction </a></li><li class="tocline"><a href="#attribute-matching" class="tocxref"><span class="secno">4.2 </span> Attribute matching </a></li><li class="tocline"><a href="#semantics-of-element-formulas" class="tocxref"><span class="secno">4.3 </span> Semantics of Element Formulas </a><ul class="toc"><li class="tocline"><a href="#entity" class="tocxref"><span class="secno">4.3.1 </span> Entity </a></li><li class="tocline"><a href="#activity" class="tocxref"><span class="secno">4.3.2 </span> Activity </a></li><li class="tocline"><a href="#agent" class="tocxref"><span class="secno">4.3.3 </span> Agent </a></li></ul></li><li class="tocline"><a href="#semantics-of-relations" class="tocxref"><span class="secno">4.4 </span> Semantics of Relations </a><ul class="toc"><li class="tocline"><a href="#generation" class="tocxref"><span class="secno">4.4.1 </span> Generation </a></li><li class="tocline"><a href="#use" class="tocxref"><span class="secno">4.4.2 </span> Use </a></li><li class="tocline"><a href="#invalidation" class="tocxref"><span class="secno">4.4.3 </span> Invalidation </a></li><li class="tocline"><a href="#association" class="tocxref"><span class="secno">4.4.4 </span> Association </a></li><li class="tocline"><a href="#start-formulas" class="tocxref"><span class="secno">4.4.5 </span> Start Formulas </a></li><li class="tocline"><a href="#end" class="tocxref"><span class="secno">4.4.6 </span> End </a></li><li class="tocline"><a href="#attribution" class="tocxref"><span class="secno">4.4.7 </span> Attribution </a></li><li class="tocline"><a href="#communication" class="tocxref"><span class="secno">4.4.8 </span>Communication</a></li><li class="tocline"><a href="#responsibility" class="tocxref"><span class="secno">4.4.9 </span> Responsibility </a></li><li class="tocline"><a href="#derivation" class="tocxref"><span class="secno">4.4.10 </span> Derivation </a><ul class="toc"><li class="tocline"><a href="#precise" class="tocxref"><span class="secno">4.4.10.1 </span> Precise </a></li><li class="tocline"><a href="#imprecise" class="tocxref"><span class="secno">4.4.10.2 </span> Imprecise </a></li></ul></li><li class="tocline"><a href="#influence" class="tocxref"><span class="secno">4.4.11 </span>Influence</a></li><li class="tocline"><a href="#specialization" class="tocxref"><span class="secno">4.4.12 </span> Specialization </a></li><li class="tocline"><a href="#alternate" class="tocxref"><span class="secno">4.4.13 </span> Alternate </a></li><li class="tocline"><a href="#membership" class="tocxref"><span class="secno">4.4.14 </span> Membership </a></li></ul></li><li class="tocline"><a href="#auxiliary-formulas" class="tocxref"><span class="secno">4.5 </span>Auxiliary formulas</a><ul class="toc"><li class="tocline"><a href="#equals" class="tocxref"><span class="secno">4.5.1 </span>Equals</a></li><li class="tocline"><a href="#precedes-and-strictly-precedes" class="tocxref"><span class="secno">4.5.2 </span>Precedes and Strictly Precedes</a></li><li class="tocline"><a href="#notnull" class="tocxref"><span class="secno">4.5.3 </span>notNull</a></li><li class="tocline"><a href="#typeof" class="tocxref"><span class="secno">4.5.4 </span>typeOf</a></li></ul></li></ul></li><li class="tocline"><a href="#theory" class="tocxref"><span class="secno">5. </span> Inferences and Constraints </a><ul class="toc"><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5.1 </span>Inferences</a></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">5.2 </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">5.2.1 </span>Uniqueness constraints</a></li><li class="tocline"><a href="#ordering-constraints" class="tocxref"><span class="secno">5.2.2 </span>Ordering constraints</a></li><li class="tocline"><a href="#typing-constraints" class="tocxref"><span class="secno">5.2.3 </span>Typing constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">5.2.4 </span>Impossibility constraints</a></li></ul></li></ul></li><li class="tocline"><a href="#soundness" class="tocxref"><span class="secno">6. </span>Soundness</a></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">A. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">B. </span>References</a><ul class="toc"><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">B.1 </span>Informative references</a></li></ul></li></ul></section>
+</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1. </span>Introduction</a><ul class="toc"><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.1 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.2 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.3 </span> Audience </a></li></ul></li><li class="tocline"><a href="#basics" class="tocxref"><span class="secno">2. </span> Basics </a><ul class="toc"><li class="tocline"><a href="#identifiers" class="tocxref"><span class="secno">2.1 </span> Identifiers </a></li><li class="tocline"><a href="#times-and-intervals" class="tocxref"><span class="secno">2.2 </span> Times and Intervals </a></li><li class="tocline"><a href="#attributes-and-values" class="tocxref"><span class="secno">2.3 </span> Attributes and Values </a></li><li class="tocline"><a href="#formulas" class="tocxref"><span class="secno">2.4 </span>Atomic Formulas</a></li><li class="tocline"><a href="#first-order-formulas" class="tocxref"><span class="secno">2.5 </span>First-Order Formulas</a></li></ul></li><li class="tocline"><a href="#structures" class="tocxref"><span class="secno">3. </span> Structures and Interpretations </a><ul class="toc"><li class="tocline"><a href="#things-1" class="tocxref"><span class="secno">3.1 </span> Things </a></li><li class="tocline"><a href="#objects-1" class="tocxref"><span class="secno">3.2 </span> Objects </a><ul class="toc"><li class="tocline"><a href="#entities-1" class="tocxref"><span class="secno">3.2.1 </span> Entities </a><ul class="toc"><li class="tocline"><a href="#plans-1" class="tocxref"><span class="secno">3.2.1.1 </span> Plans </a></li></ul></li><li class="tocline"><a href="#activities-1" class="tocxref"><span class="secno">3.2.2 </span> Activities </a></li><li class="tocline"><a href="#agents-1" class="tocxref"><span class="secno">3.2.3 </span> Agents </a></li><li class="tocline"><a href="#interactions-1" class="tocxref"><span class="secno">3.2.4 </span> Interactions </a><ul class="toc"><li class="tocline"><a href="#events-1" class="tocxref"><span class="secno">3.2.4.1 </span> Events </a></li><li class="tocline"><a href="#associations-1" class="tocxref"><span class="secno">3.2.4.2 </span> Associations </a></li><li class="tocline"><a href="#communications" class="tocxref"><span class="secno">3.2.4.3 </span>Communications</a></li><li class="tocline"><a href="#delegations" class="tocxref"><span class="secno">3.2.4.4 </span>Delegations</a></li><li class="tocline"><a href="#derivations-1" class="tocxref"><span class="secno">3.2.4.5 </span> Derivations </a></li></ul></li></ul></li><li class="tocline"><a href="#relations" class="tocxref"><span class="secno">3.3 </span> Relations </a><ul class="toc"><li class="tocline"><a href="#derivation-paths-and-derivedfrom" class="tocxref"><span class="secno">3.3.1 </span> Derivation paths and DerivedFrom </a></li></ul></li><li class="tocline"><a href="#putting-it-all-together" class="tocxref"><span class="secno">3.4 </span> Putting it all together </a></li><li class="tocline"><a href="#interpretations" class="tocxref"><span class="secno">3.5 </span> Interpretations </a></li></ul></li><li class="tocline"><a href="#semantics" class="tocxref"><span class="secno">4. </span> Semantics </a><ul class="toc"><li class="tocline"><a href="#satisfaction" class="tocxref"><span class="secno">4.1 </span> Satisfaction </a></li><li class="tocline"><a href="#attribute-matching" class="tocxref"><span class="secno">4.2 </span> Attribute matching </a></li><li class="tocline"><a href="#semantics-of-element-formulas" class="tocxref"><span class="secno">4.3 </span> Semantics of Element Formulas </a><ul class="toc"><li class="tocline"><a href="#entity" class="tocxref"><span class="secno">4.3.1 </span> Entity </a></li><li class="tocline"><a href="#activity" class="tocxref"><span class="secno">4.3.2 </span> Activity </a></li><li class="tocline"><a href="#agent" class="tocxref"><span class="secno">4.3.3 </span> Agent </a></li></ul></li><li class="tocline"><a href="#semantics-of-relations" class="tocxref"><span class="secno">4.4 </span> Semantics of Relations </a><ul class="toc"><li class="tocline"><a href="#generation" class="tocxref"><span class="secno">4.4.1 </span> Generation </a></li><li class="tocline"><a href="#use" class="tocxref"><span class="secno">4.4.2 </span> Use </a></li><li class="tocline"><a href="#invalidation" class="tocxref"><span class="secno">4.4.3 </span> Invalidation </a></li><li class="tocline"><a href="#association" class="tocxref"><span class="secno">4.4.4 </span> Association </a></li><li class="tocline"><a href="#start-formulas" class="tocxref"><span class="secno">4.4.5 </span> Start Formulas </a></li><li class="tocline"><a href="#end" class="tocxref"><span class="secno">4.4.6 </span> End </a></li><li class="tocline"><a href="#attribution" class="tocxref"><span class="secno">4.4.7 </span> Attribution </a></li><li class="tocline"><a href="#communication" class="tocxref"><span class="secno">4.4.8 </span>Communication</a></li><li class="tocline"><a href="#responsibility" class="tocxref"><span class="secno">4.4.9 </span> Responsibility </a></li><li class="tocline"><a href="#derivation" class="tocxref"><span class="secno">4.4.10 </span> Derivation </a><ul class="toc"><li class="tocline"><a href="#precise" class="tocxref"><span class="secno">4.4.10.1 </span> Precise </a></li><li class="tocline"><a href="#imprecise" class="tocxref"><span class="secno">4.4.10.2 </span> Imprecise </a></li></ul></li><li class="tocline"><a href="#influence" class="tocxref"><span class="secno">4.4.11 </span>Influence</a></li><li class="tocline"><a href="#specialization" class="tocxref"><span class="secno">4.4.12 </span> Specialization </a></li><li class="tocline"><a href="#alternate" class="tocxref"><span class="secno">4.4.13 </span> Alternate </a></li><li class="tocline"><a href="#membership" class="tocxref"><span class="secno">4.4.14 </span> Membership </a></li></ul></li><li class="tocline"><a href="#auxiliary-formulas" class="tocxref"><span class="secno">4.5 </span>Auxiliary formulas</a><ul class="toc"><li class="tocline"><a href="#equals" class="tocxref"><span class="secno">4.5.1 </span>Equals</a></li><li class="tocline"><a href="#precedes-and-strictly-precedes" class="tocxref"><span class="secno">4.5.2 </span>Precedes and Strictly Precedes</a></li><li class="tocline"><a href="#notnull" class="tocxref"><span class="secno">4.5.3 </span>notNull</a></li><li class="tocline"><a href="#typeof" class="tocxref"><span class="secno">4.5.4 </span>typeOf</a></li></ul></li></ul></li><li class="tocline"><a href="#theory" class="tocxref"><span class="secno">5. </span> Inferences and Constraints </a><ul class="toc"><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">5.1 </span>Inferences</a></li><li class="tocline"><a href="#constraints" class="tocxref"><span class="secno">5.2 </span>Constraints</a><ul class="toc"><li class="tocline"><a href="#uniqueness-constraints" class="tocxref"><span class="secno">5.2.1 </span>Uniqueness constraints</a></li><li class="tocline"><a href="#ordering-constraints" class="tocxref"><span class="secno">5.2.2 </span>Ordering constraints</a></li><li class="tocline"><a href="#typing-constraints" class="tocxref"><span class="secno">5.2.3 </span>Typing constraints</a></li><li class="tocline"><a href="#impossibility-constraints" class="tocxref"><span class="secno">5.2.4 </span>Impossibility constraints</a></li></ul></li></ul></li><li class="tocline"><a href="#soundness" class="tocxref"><span class="secno">6. </span>Soundness</a></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">A. </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">B. </span>References</a><ul class="toc"><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">B.1 </span>Informative references</a></li></ul></li></ul></section>
 
 
 
@@ -946,7 +951,7 @@
 [<cite><a class="bibref" href="#bib-PROV-CONSTRAINTS">PROV-CONSTRAINTS</a></cite>] that
 specifies definitions, inferences, and constraints that can be used to
 reason about PROV documents, or determine their validity.  This document
-provides a reference formal semantics of PROV, providing a formal
+provides a naive formal semantics of PROV, providing a formal
 counterpart to the informal descriptions and motivations given
 elsewhere in PROV specifications.</p>
 
@@ -997,19 +1002,33 @@
 building upon PROV.  It is intended as an exploration of a <b>reference</b>
 semantics for PROV, not a definitive specification of the  <b>only</b>
 semantics of PROV.  </p>
-
-<p> Nevertheless, the reference semantics does have appealing
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  <p>Clarify role of the semantics - too defensive?</p>
+  </div></div>
+
+<p> Although it is a work in progress, the naive semantics has some appealing
 properties.  Specifically, it provides a declarative counterpart to
 the operational definition of validity taken in PROV-CONSTRAINTS.  In
 the specification, validity is defined via a normalization process
 followed by constraint checking on the normal form.  This approach was adopted
 to keep the specification closer to implementations, although other
 implementations are possible and allowed.  In addition to providing a
-reference semantics, this document shows that the operational
+naive semantics, this document shows that the operational
 presentation of PROV validity checking is sound with respect to
 declarative presentation adopted here.  This could help justify
 alternative approaches to validity checking.</p>
 
+<p>This document mostly considers the semantics of PROV statements and
+  instances.  PROV documents can consist of multiple instances, and
+  the semantics does not (as yet) cover PROV documents, but the
+  semantics can be used on each instance in a document separately,
+  just as PROV-CONSTRAINTS specifies that each instance in a document
+  is to be validated separately.
+  So, in the rest of this document, we do not discuss PROV documents.
+  The semantics of other features of PROV, such as dictionaries
+  [<cite><a class="bibref" href="#bib-PROV-DICTIONARY">PROV-DICTIONARY</a></cite>] and linking across bundles [<cite><a class="bibref" href="#bib-PROV-LINKS">PROV-LINKS</a></cite>], are
+  beyond the scope of this document.  </p>
+  
 <section id="structure-of-this-document"> <h3><span class="secno">1.2 </span>Structure of this document</h3> <p>
 
 </p>
@@ -1028,16 +1047,13 @@
   <li><a href="#theory">Section 5</a> presents the inferences and
   constraints from PROV-CONSTRAINTS as first-order formulas, and gives
   brief justifications for their soundness.</li>
-  <li><a href="#soundness">Section 6</a> relates the PROV notion of
-  validity to the logical notion of consistency.  A PROV instance is
-  valid if and only if its corresponding first-order theory is
-  satisfiable.</li>
+  <li><a href="#soundness">Section 6</a> summarizes the main result: soundness of
+the theory introduced in section 5 with respect to reference
+  semantics.  Completeness does not hold for the naive semantics</li>
 </ul>
 <div class="note"><div class="note-title"><span>Note</span></div><div class="">
-  Completeness direction above doesn't hold for current semantics,
-  because attributes assumed to be single-valued; for
-  example, <span class="MathJax_Preview">entity(id,[a=1,a=2])</span><script type="math/tex" id="MathJax-Element-3">entity(id,[a=1,a=2])</script> is valid but doesn't have a
-  reference model.
+<p>TODO: We would like to say something stronger here, such as a
+  completeness result, but this will take more work.</p>
   </div></div>
 
 </section>
@@ -1116,37 +1132,52 @@
 <section id="identifiers">
 <h3><span class="secno">2.1 </span> Identifiers </h3>
 
-<p>A lowercase symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-4-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">,</mo><mi>y</mi><mo stretchy="false">,</mo><mo>.</mo><mo>.</mo><mo>.</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-4">x,y,...</script> on its own denotes an identifier.
-Identifiers may or may not be URIs.  Identifiers are viewed as variables in logic (or blank nodes in RDF): just because we have two different identifiers <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-5-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-5">x</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-6-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-6">y</script> doesn't tell us that they denote different things, since we could discover that they are actually the same later.  We write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-7-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-7">Identifiers</script> for the set of identifiers of interest in a given situation (typically, the set of identifiers present in the PROV instance of interest).
+<p>A lowercase symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-3-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">,</mo><mi>y</mi><mo stretchy="false">,</mo><mo>.</mo><mo>.</mo><mo>.</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-3">x,y,...</script> on its own denotes an identifier.
+Identifiers may or may not be URIs.  Identifiers are viewed as
+variables from the point of view of logic: they denote objects, but
+just because we have two different identifiers <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-4-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-4">x</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-5-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-5">y</script> doesn't
+tell us that they denote different objects, since we could discover
+that they are actually the same later.  We write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-6-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-6">Identifiers</script> for the
+set of identifiers of interest in a given situation (typically, the
+set of identifiers present in the PROV instance of interest).
 </p>
 </section>
 
 <section id="times-and-intervals">
 <h3><span class="secno">2.2 </span> Times and Intervals </h3>
 
-<p>We assume a linearly ordered set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-8-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mo stretchy="false">≤</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-8">(Times,\leq)</script> of time instants.  For convenience we assume the order is total or linear order, corresponding to a linear timeline; however, PROV does not assume that time is linear and events could be partially ordered and not necessarily reconciled to a single global clock.  
+<p>We assume a linearly ordered set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-7-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">,</mo><mo stretchy="false">≤</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-7">(Times,\leq)</script> of time instants.  For convenience we assume the order is total or linear order, corresponding to a linear timeline; however, PROV does not assume that time is linear and events could be partially ordered and not necessarily reconciled to a single global clock.  
 </p>
-<p>We also consider a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-9-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-9">Intervals</script> of closed intervals of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-10-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mi>t</mi><mo stretchy="false">∣</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≤</mo><mi>t</mi><mo stretchy="false">≤</mo><msub><mi>t</mi><mn>2</mn></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-10">\{t \mid t_1 \leq t \leq t_2\}</script>.
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  Discuss implications of restricting attention to a linear order.
+  </div></div>
+
+<p>We also consider a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-8-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-8">Intervals</script> of closed intervals of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-9-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mi>t</mi><mo stretchy="false">∣</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≤</mo><mi>t</mi><mo stretchy="false">≤</mo><msub><mi>t</mi><mn>2</mn></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-9">\{t \mid t_1 \leq t \leq t_2\}</script>.
 </p>
 </section>
 
 <section id="attributes-and-values">
 <h3><span class="secno">2.3 </span> Attributes and Values </h3>
 
-<p>We assume a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-11-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-11">Attributes</script> of attribute labels and a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-12-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-12">Values</script>
+<p>We assume a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-10-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-10">Attributes</script> of attribute labels and a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-11-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-11">Values</script>
 of possible values of attributes.  To allow for the fact that some
 attributes can have undefined or multiple values, we sometimes use the set
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-13-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-13">P(Value)</script>, that is, the set of sets of values.
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-12-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-12">P(Value)</script>, that is, the set of sets of values.
 </p> </section>
 
 <section id="formulas">
 <h3><span class="secno">2.4 </span>Atomic Formulas</h3>
 
-<p>The following atomic formulas correspond to the statements of PROV-DM.  We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-14-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-14">r(id,a_1,\ldots,a_n)</script> instead of the semicolon notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-15-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">;</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-15">r(id;a_1,\ldots,a_n)</script>.
+<p>The following atomic formulas correspond to the statements of PROV-DM.  We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-13-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-13">r(id,a_1,\ldots,a_n)</script> instead of the semicolon notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-14-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">;</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-14">r(id;a_1,\ldots,a_n)</script>.
 </p>
-<p>Each parameter is either an identifier, a constant (e.g. a time or other literal value in an attribute list), or a null symbol "-".  Null symbols can only appear in the specified arguments in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-16-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-16">wasAssociatedWith</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-17-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-17">wasDerivedFrom</script>, as shown in the grammar below.
+<p>Each parameter is either an identifier, a constant (e.g. a time or
+  other literal value in an attribute list), or a null symbol "-".
+  Time parameters (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-15-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-15">st,et</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-16-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-16">activity</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-17-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-17">t</script> in generation,
+  usage, invalidation, start and end) are always constant time
+  literals.  Placeholder symbols <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-18-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-18">-</script> can only appear in the specified arguments
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-19-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-19">pl</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-20-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-20">wasAssociatedWith</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-21-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-21">a,g,u</script> in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-22-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-22">wasDerivedFrom</script>, as shown in the grammar below.
 </p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-18-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi>a</mi><mi>t</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>c</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>e</mi><mi>l</mi><mi>e</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>r</mi><mi>e</mi><mi>l</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>u</mi><mi>x</mi><mi>i</mi><mi>l</mi><mi>i</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd><mi>e</mi><mi>l</mi><mi>e</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mi>e</mi><mi>l</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>f</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo 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stretchy="false">|</mo></mrow></mtd><mtd><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mi>u</mi><mi>x</mi><mi>i</mi><mi>l</mi><mi>i</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>x</mi><mo 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stretchy="false">[</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mn>1</mn></msub><mo stretchy="false">=</mo><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>n</mi></msub><mo stretchy="false">=</mo><msub><mi>v</mi><mi>n</mi></msub><mo stretchy="false">]</mo></mtd></mtr><mtr><mtd><mi>t</mi><mi>y</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-23">
 \begin{array}{rcl}
   atomic\_formula & {::=}& element\_formula\\
           & | & relation\_formula\\
@@ -1159,8 +1190,8 @@
           &{::=}& wasGeneratedBy(id,e,a,t,attrs)\\
           & |&  used(id,e,a,t,attrs)\\
           & |&  wasInvalidatedBy(id,e,a,t,attrs)\\
-          & |&  wasStartedBy(id,a_2,e,a_1,attrs)\\
-          & |&  wasEndedBy(id,a_2,e,a_1,attrs)\\
+          & |&  wasStartedBy(id,a_2,e,a_1,t,attrs)\\
+          & |&  wasEndedBy(id,a_2,e,a_1,t,attrs)\\
           & |&  wasAssociatedWith(id,ag,act,pl,attrs)\\
           & |&  wasAssociatedWith(id,ag,act,-,attrs)\\
           & |&  wasAttributedTo(id,e,ag,attrs)\\
@@ -1186,7 +1217,18 @@
 &|& prov:EmptyCollection
 \end{array}
 </script>
-
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  Remove prefixes from prov:Collection and prov:EmptyCollection?
+  </div></div>
+
+  <div class="note"><div class="note-title"><span>Note</span></div><div class="">
+    Restate that we are not modeling documents/bundles, however eachi
+    instance can be modeled separately.
+    </div></div>
+
+    <div class="note"><div class="note-title"><span>Note</span></div><div class="">
+      similar question: can we try to handle mentionOf?
+      </div></div>
 </section>
 
 <section id="first-order-formulas">
@@ -1194,7 +1236,7 @@
 
 <p>We also consider the usual connectives and quantifiers of
 first-order logic [<cite><a class="bibref" href="#bib-Logic">Logic</a></cite>].</p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-19-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="italic">ϕ</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>a</mi><mi>t</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>c</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">¬</mi><mtext>&nbsp;</mtext><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∨</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">⇒</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-19">
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-24-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="italic">ϕ</mi></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">::=</mo></mrow></mtd><mtd><mi>a</mi><mi>t</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>c</mi><mi mathvariant="normal">_</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">¬</mi><mtext>&nbsp;</mtext><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∨</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">⇒</mo><msub><mi mathvariant="italic">ϕ</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-24">
 \begin{array}{rcl}
   \phi &{::=}& atomic\_formula\\
 & | & True\\
@@ -1233,32 +1275,36 @@
 <h3><span class="secno">3.1 </span> Things </h3> 
 
 <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Containment of things / collections? (for hadMember).</div></div>
-<p><em>Things</em> are things in the world.  Each thing has a lifetime during which it exists and attributes whose values can change over time.
+<p><em>Things</em>  is a set of things in the situation being modeled.  Each thing has a lifetime during which it exists and attributes whose values can change over time.
 </p>
-<p>To model this, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-20-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-20">W</script> includes:
+<p>To model this, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-25-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-25">W</script> includes:
 </p>
 <div class="component" id="things" data-count="1" data-title="Component 1 (things)"><div class="ruleTitle"><a class="internalDFN" href="#things">Component 1 (things)</a></div><ol>
-  <li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-21-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-21">Things</script> of things</li>
-  <li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-22-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-22">lifetime : Things \to Intervals</script> from objects to time intervals</li>
-  <li>a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-23-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-23">value : Things \times Attributes \times Times \to P(Values)</script>
+  <li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-26-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-26">Things</script> of things</li>
+  <li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-27-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">→</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-27">lifetime : Things \to Intervals</script> from things to time intervals</li>
+  <li>a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-28-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-28">value : Things \times Attributes \times Times \to P(Values)</script>
 </li>
 </ol>
 </div>
 <p>
-The range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-24-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-24">value</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-25-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-25">P(Values)</script>, indicating that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-26-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-26">value</script>
-is essentially a multi-valued that returns a set of values (possibly empty).    When <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-27-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-27">value(x,a,t) =
-\emptyset</script>, we say that attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-28-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-28">a</script> is undefined for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-29-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-29">x</script> at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-30-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-30">t</script>.</p>
+The range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-29-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-29">value</script> is the set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-30-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-30">P(Values)</script>, indicating that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-31-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-31">value</script>
+is essentially a multi-valued that returns a set of values (possibly empty).    When <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-32-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-32">value(x,a,t) =
+\emptyset</script>, we say that attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-33-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-33">a</script> is undefined for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-34-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-34">x</script> at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-35-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-35">t</script>.</p>
 
 <p>Note that this description does not say what the structure of a
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-31-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-31">Thing</script> is, only how it may be described in terms of its time interval
-and attribute values.  An object could just be a record of fixed
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-36-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-36">Thing</script> is, only how it may be described in terms of its time interval
+and attribute values.  A thing could be a record of fixed
 attribute values; it could be a bear; it could be the Royal Society;
-it could be a transcendental number like <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-32-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">π</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-32">\pi</script>.  All that matters from
-our point of view is that we know how to map the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-33-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-33">Thing</script> to its time interval and attribute mapping.
+it could be a transcendental number like <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-37-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">π</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-37">\pi</script>.  All that matters from
+our point of view is that we know how to map the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-38-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-38">Thing</script> to its time interval and attribute mapping.
 </p>
 
 
-<p>It is possible for two Things to be indistinguishable by their attribute values and lifetime, but have different identity.
+<p>The identity of a Thing is not observable through its attributes or
+lifetime, so it is possible for two different Things to be indistinguishable by their
+attribute values and lifetime.  That is, if the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-39-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>T</mi><mn>1</mn></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-39">Things = \{T_0,T_1\}</script> and the attributes are
+specified as <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-40-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>T</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-40">value(T_0,a,t) = value(T_1,a,t)</script> for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-41-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo stretchy="false">∈</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-41">t\in
+Times</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-42-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">∈</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-42">a \in Attributes</script>, this does not imply that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-43-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>0</mn></msub><mo stretchy="false">=</mo><msub><mi>T</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-43">T_0 = T_1</script>.
 </p>
 
 
@@ -1267,76 +1313,103 @@
 <section id="objects-1">
 <h3><span class="secno">3.2 </span> Objects </h3>
 
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  TODO: Add text explaining the relationship between Things and
+  Objects.
+</div></div>
+
 <p>
-An <em>Object</em> is described by a time interval and attributes with unchanging values.  Objects encompass entities, interactions, and activities.
+An <em>Object</em> is described by a time interval and attributes with
+fixed values.  Objects encompass entities, activities, agents, and
+interactions (i.e., usage, generation, and other events or influence relations).
 To model this, a structure includes:
 </p>
 
 <div class="component" id="objects" data-count="2" data-title="Component 2 (objects)"><div class="ruleTitle"><a class="internalDFN" href="#objects">Component 2 (objects)</a></div>
-  <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-34-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-34">Objects</script> 
-</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-35-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-35">lifetime : Objects \to Intervals</script> from objects to time intervals
-</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-36-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-36">value : Objects \times Attributes \to P(Values)</script>
+  <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-44-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-44">Objects</script> 
+</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-45-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-45">lifetime : Objects \to Intervals</script> from objects to time intervals
+</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-46-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">:</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-46">value : Objects \times Attributes \to P(Values)</script>
 </li></ol>
 </div>
 
-<p>Intuitively, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-37-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-37">lifetime(e)</script> is the time interval during which object
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-38-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-38">e</script> exists.  The set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-39-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-39">value(e,a)</script> is the set of values of attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-40-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-40">a</script> during the object's lifetime.
+<p>Intuitively, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-47-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-47">lifetime(e)</script> is the time interval during which object
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-48-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-48">e</script> exists.  The set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-49-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-49">value(e,a)</script> is the set of values of attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-50-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-50">a</script> during the object's lifetime.
 </p>
 
-<p>As with <em>Things</em>, the range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-41-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-41">value</script> is sets of values,
-making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-42-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-42">value</script> effectively a multivalued function.  It is also possible to have two different objects that are indistinguishable by their attributes and time intervals.  Objects are not things, and the sets of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-43-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-43">Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-44-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-44">Things</script> are disjoint; however, certain objects, namely entities, are linked to things.
-
+<p>As with <em>Things</em>, the range of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-51-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-51">value</script> is sets of values,
+making <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-52-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-52">value</script> effectively a multivalued function.  It is also
+possible to have two different objects that are indistinguishable by
+their attributes and time intervals.  Objects are not things, and the
+sets of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-53-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-53">Objects</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-54-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-54">Things</script> are disjoint; however, certain objects,
+namely entities, are associated with things.
 </p>
+
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  Disjointness between object and thing is not necessary but is
+  assumed in order to avoid confusion between the different categories
+  (time-varying vs fixed); nothing changes if we allow them to overlap.
+  </div></div>
 <section id="entities-1">
 <h4><span class="secno">3.2.1 </span> Entities </h4>
 
-An <em>entity</em> is a kind of object that describes a time-slice of a thing, during which some of the thing's attributes are fixed. We assume:
+<p>An <em>entity</em> is a kind of object that describes a time-slice of a thing, during which some of the thing's attributes are fixed. We assume:</p>
 
 <div class="component" id="entities" data-count="3" data-title="Component 3 (entities)"><div class="ruleTitle"><a class="internalDFN" href="#entities">Component 3 (entities)</a></div>
-  <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-45-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-45">Entities \subseteq Objects</script> of entities, disjoint from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-46-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-46">Activities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-47-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-47">Events</script> below.
-</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-48-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-48">thingOf : Entities \to Things</script> that associates each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-49-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-49">Entity</script> with a <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-50-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-50">Thing</script>, such that for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-51-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-51">t \in lifetime(obj)</script>, and for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-52-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-52">a</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-53-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-53">value(obj,a) \subseteq value(thingOf(obj),a,t)</script>.
-</li><li> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-54-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-54">lifetime(e) \subseteq lifetime(t)</script>.
+  <ol><li> a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-55-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-55">Entities \subseteq Objects</script> of entities, disjoint from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-56-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-56">Activities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-57-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-57">Events</script> below.
+</li><li> a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-58-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">:</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-58">thingOf : Entities \to Things</script> that associates each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-59-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-59">Entity</script> with a <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-60-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-60">Thing</script>, such that for each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-61-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-61">t \in lifetime(obj)</script>, and for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-62-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-62">a</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-63-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-63">value(obj,a) \subseteq value(thingOf(obj),a,t)</script>.
+</li><li> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-64-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-64">lifetime(e) \subseteq lifetime(t)</script>.
 </li></ol>
 </div>
 
 <div class="remark"><p> Although both entities and things can have
   undefined or multiple attribute values, their meaning is slightly
-  different: for a thing, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-55-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-55">value(x,a,t) = \emptyset</script> means that the
-  attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-56-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-56">a</script> has no value at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-57-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-57">t</script>, whereas for an entity,
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-58-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-58">value(x,a) = \emptyset</script> only means that the entity does not record
-  a fixed value for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-59-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-59">a</script> forthe associated thing.  This does not imply
-  that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-60-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-60">value(thingOf(e),a,t) = \emptyset</script> when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-61-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-61">t \in lifetime(e)</script>.
-</p>
-  <p>Furthermore, all of the attribute values of the entity must be
-  present in the associated thing throughout the lifetime of the entity.
-For example, suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-62-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-62">value(thingOf(e),a,t)</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-63-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-63">\{1\}</script> at some
-time in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-64-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-64">lifetime(e)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-65-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-65">value(thingOf(e),a,t') = \{2\}</script> at some
-  other time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-66-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-66">t'</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-67-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-67">value(e,a)</script> must be <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-68-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-68">\emptyset</script> because
+  different: for a thing, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-65-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-65">value(x,a,t) = \emptyset</script> means that the
+  attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-66-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-66">a</script> has no value at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-67-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-67">t</script>, whereas for an entity,
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-68-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-68">value(x,a) = \emptyset</script> only means that the thing associated to
+  entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-69-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-69">x</script> does not have a
+  fixed value for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-70-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-70">a</script> during the lifetime of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-71-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-71">x</script>.  This does not imply
+  that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-72-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-72">value(thingOf(e),a,t) = \emptyset</script> when <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-73-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-73">t \in lifetime(e)</script>.
+  </p>
+
+  <p>Furthermore, all of the attribute values of the entity must
+  be present in the associated thing throughout the lifetime of the
+  entity.  For example, suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-74-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-74">value(thingOf(e),a,t)</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-75-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-75">\{1\}</script> at
+  some time in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-76-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-76">lifetime(e)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-77-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msup><mi>t</mi><mo>′</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-77">value(thingOf(e),a,t') = \{2\}</script> at
+  some other time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-78-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-78">t'</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-79-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-79">value(e,a)</script> must be <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-80-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-80">\emptyset</script> because
   there is no other set of values that is simultaneously contained in
-  both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-69-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-69">\{1\}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-70-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-70">\{2\}</script>.
-</p>
-  </div>
-
+  both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-81-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-81">\{1\}</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-82-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-82">\{2\}</script>.  </p> </div>
+
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  Can we give further intuiton for the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-83-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-83">value(obj,a) \subseteq
+  value(thingOf(obj),a,t)</script> and what it tells us about objects
+  vs. things?
+  </div></div>
+  
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+TODO:   Is there a reason why only Entities are assciated with Things,
+  rather than allowing all Objects to be associated with Things?
+  </div></div>
+  
 <section id="plans-1">  
 <h5><span class="secno">3.2.1.1 </span> Plans </h5>
 <p>We identify a specific subset of the entities called
   <em>plans</em>:</p>
 <div class="component" id="plans" data-count="4" data-title="Component 4 (plans)"><div class="ruleTitle"><a class="internalDFN" href="#plans">Component 4 (plans)</a></div>
- <p> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-71-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-71">Plans \subseteq Entities</script> of plans.</p>
+ <p> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-84-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-84">Plans \subseteq Entities</script> of plans.</p>
   </div>
 </section>
 
   </section>
 
-    <section id="actvities">
-<h4><span class="secno">3.2.2 </span> Actvities </h4>
+    <section id="activities-1">
+<h4><span class="secno">3.2.2 </span> Activities </h4>
 
 
 <p>An <em>activity</em> is an object that encompasses a set of events.  We introduce
 </p>
 <div class="component" id="activities" data-count="5" data-title="Component 5 (activities)"><div class="ruleTitle"><a class="internalDFN" href="#activities">Component 5 (activities)</a></div>
-  <ol><li>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-72-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-72">Activities \subseteq Objects</script> of activities.</li>
-  <li> Activities are disjoint from Entities: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-73-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∩</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-73">Entities\cap Activities
+  <ol><li>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-85-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-85">Activities \subseteq Objects</script> of activities.</li>
+  <li> Activities are disjoint from Entities: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-86-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∩</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-86">Entities\cap Activities
   = \emptyset</script>.</li>
   </ol>
 </div></section>
@@ -1345,40 +1418,52 @@
 <h4><span class="secno">3.2.3 </span> Agents </h4>
 
 <p>An agent is an object that can act, by controlling, starting,
-  ending, or participating in activities.  Agents can act on behalf of
-  other agents. An agent can be an entity, an activity, or neither; an
+  ending, or participating in activities.  An agent is something that
+  bears some form of responsibility for an activity taking place, for
+  the existence of an entity, or for another agent's activity.  Agents can act on behalf of
+  other agents. An agent may be a particular type of entity or activity; an
   agent cannot be both entity and activity because the sets of
   entities and activities are disjoint.  We introduce:
 </p>
 <div class="component" id="agents" data-count="6" data-title="Component 6 (agents)"><div class="ruleTitle"><a class="internalDFN" href="#agents">Component 6 (agents)</a></div>
-  <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-74-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-74">Agents \subseteq Objects</script> of agents.</p>
+  <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-87-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-87">Agents \subseteq Objects</script> of agents.</p>
   </div>
-</section>
+  <div class="remark">
+    <p>There is no requirement that every agent is either an activity
+  or an entity. </p>
+</div></section>
 
 
 <section id="interactions-1">
 <h4><span class="secno">3.2.4 </span> Interactions </h4>
 
-<p>We consider a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-75-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-75">Interactions \subseteq Objects</script> which are split into
+<p>We consider a set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-88-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-88">Interactions \subseteq Objects</script> which are split into
   <em>Events</em> connecting entities and activities,
   <em>Associations</em> between agents and activities,
   <em>Communications</em> between pairs of activities,
-  <em>Delegations</em> between pairs of agents, and <em>Derivations</em> that describe chains of generation and usage steps.  (The first two sets may overlap.)  Interactions are disjoint from entities, activities and agents.
+  <em>Delegations</em> between pairs of agents, and
+  <em>Derivations</em> that describe chains of generation and usage
+  steps.  These kinds of interactions are discussed further below.  Interactions are disjoint from entities, activities and agents.
 </p>
 <div class="component" id="interactions" data-count="7" data-title="Component 7 (interactions)"><div class="ruleTitle"><a class="internalDFN" href="#interactions">Component 7 (interactions)</a></div>
-  <ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-76-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-76">Interactions = Events \cup Associations \cup
+  <ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-89-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-89">Interactions = Events \cup Associations \cup
   Communications \cup Delegations \cup Derivations \subseteq Objects</script>
 </li>
-<li> A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-77-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">:</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mo fence="false" stretchy="false">{</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi>S</mi><mi>o</mi><mi>u</mi><mi>r</mi><mi>c</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-77">type: Interactions \to
-  \{start,end,usage,generation,invalidation,derivation,version,quotation,primarySource,attribution,delegation\}</script>.
+<li> A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-90-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">:</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mo fence="false" stretchy="false">{</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>r</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi>S</mi><mi>o</mi><mi>u</mi><mi>r</mi><mi>c</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-90">type: Interactions \to
+  \{start,end,usage,generation,invalidation,derivation,revision,quotation,primarySource,attribution,delegation\}</script>.
 </li>
-<li> The sets <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-78-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-78">Events</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-79-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-79">Associations</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-80-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-80">Communications</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-81-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-81">Delegations</script>
-  and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-82-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-82">Derivations</script> are all disjoint.
+<li> The sets <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-91-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-91">Events</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-92-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-92">Associations</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-93-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>u</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-93">Communications</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-94-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-94">Delegations</script>
+  and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-95-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-95">Derivations</script> are all disjoint.
 </li><li> Interactions are disjoint from entities, agents and
-activities:  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-83-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∩</mo><mo stretchy="false">(</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-83">Interactions \cap (Entities \cup Activities \cup Agents) = \emptyset</script>
+activities:  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-96-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">∩</mo><mo stretchy="false">(</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">∪</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">∅</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-96">Interactions \cap (Entities \cup Activities \cup Agents) = \emptyset</script>
 </li></ol>
 </div>
 
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  Explain why the different subsets of interactions are disjoint.
+  This is necessary in order for constraint 53 to hold.
+  </div></div>
+
 <section id="events-1">
 <h5><span class="secno">3.2.4.1 </span> Events </h5>
 
@@ -1387,11 +1472,11 @@
 agent).  Events have types including usage, generation, invalidation, starting and ending.  Events are instantaneous.  We introduce:
 </p>
 <div class="component" id="events" data-count="8" data-title="Component 8 (events)"><div class="ruleTitle"><a class="internalDFN" href="#events">Component 8 (events)</a></div>
-<ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-84-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-84">Events \subseteq Interactions</script> of events, such that
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-85-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-85">type(evt) \in \{start,end,generation,usage,invalidation\}</script> if and
-  only of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-86-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-86">evt \in Events</script>.
-</li><li> A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-87-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-87">time : Events \to Times</script> giving the time of each event; i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-88-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-88">lifetime(evt) = \{time(t)\}</script>.
-</li><li> The derived ordering on events given by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-89-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≤</mo><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>2</mn></msub><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">≤</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-89">evt_1 \leq evt_2 \iff time(evt_1) \leq time(evt_2)</script>
+<ol><li> A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-97-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-97">Events \subseteq Interactions</script> of events, such that
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-98-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-98">type(evt) \in \{start,end,generation,usage,invalidation\}</script> if and
+  only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-99-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-99">evt \in Events</script>.
+</li><li> A function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-100-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">:</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">→</mo><mi>T</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-100">time : Events \to Times</script> giving the time of each event; i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-101-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-101">lifetime(evt) = \{time(evt)\}</script>.
+</li><li> The derived ordering on events given by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-102-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≤</mo><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>2</mn></msub><mspace width="thickmathspace"></mspace><mo stretchy="false">⟺</mo><mspace width="thickmathspace"></mspace><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">≤</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-102">evt_1 \leq evt_2 \iff time(evt_1) \leq time(evt_2)</script>
 </li></ol>
 </div>
 </section>
@@ -1402,12 +1487,12 @@
 <p>An <em>Association</em> is an interaction relating an agent to an activity.  To model associations, we introduce:
 </p>
 <div class="component" id="associations" data-count="9" data-title="Component 9 (associations)"><div class="ruleTitle"><a class="internalDFN" href="#associations">Component 9 (associations)</a></div>
-  <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-90-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-90">Associations \subseteq Interactions</script>, such that
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-91-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-91">type(assoc) = association</script> if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-92-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-92">assoc \in Associations</script>.
+  <p>A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-103-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-103">Associations \subseteq Interactions</script>, such that
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-104-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-104">type(assoc) = association</script> if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-105-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-105">assoc \in Associations</script>.
 </p>
   </div>
   
-<p>Associations are used below in the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-93-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-93">ActsFor</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-94-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-94">AssociatedWith</script> relations.
+<p>Associations are used below in the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-106-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-106">ActsFor</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-107-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-107">AssociatedWith</script> relations.
 
 
 </p></section>
@@ -1427,12 +1512,15 @@
 <p>A <em>Derivation</em> is an interaction chaining one or more generation and use steps.  
 </p>
 <div class="component" id="derivations" data-count="10" data-title="Component 10 (derivations)"><div class="ruleTitle"><a class="internalDFN" href="#derivations">Component 10 (derivations)</a></div>
-<p>  A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-95-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-95">Derivations \subseteq Interactions</script>, such that
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-96-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi>S</mi><mi>o</mi><mi>u</mi><mi>r</mi><mi>c</mi><mi>e</mi><mo stretchy="false">,</mo><mi>q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-96">type(deriv) \in \{derivation, version, primarySource,quotation\}</script>
-  if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-97-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-97">deriv \in Derivations</script>.
+<p>  A set <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-108-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">⊆</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-108">Derivations \subseteq Interactions</script>, such that
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-109-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>r</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>y</mi><mi>S</mi><mi>o</mi><mi>u</mi><mi>r</mi><mi>c</mi><mi>e</mi><mo stretchy="false">,</mo><mi>q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-109">type(deriv) \in \{derivation, revision, primarySource,quotation\}</script>
+  if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-110-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-110">deriv \in Derivations</script>.
 </p></div>
 <p>See below for the associated derivation path and DerivedFrom relation.
 </p>
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Clarify that existence of a chained generation
+  and use step does not necessarily imply derivation</div></div>
+  
 </section>
 </section>
 </section>
@@ -1443,12 +1531,12 @@
 <h3 id="simple-relations"> Simple relations </h3>
 <p>The entities, interactions, and activities in a structure are related in the following ways:
 </p>
-<ol><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-98-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-98">Used \subseteq Events \times Entities</script> saying when an event used an entity.  An event can use at most one entity, and if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-99-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-99">(evt,e)\in Used</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-100-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-100">time(evt) \in lifetime(e)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-101-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>u</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-101">type(g) = use</script> must hold.
-</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-102-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-102">Generated \subseteq Events \times Entities</script> saying when an event generated an entity.  An event can generate at most one entity, and if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-103-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-103">(evt,e)\in Generated</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-104-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-104">min(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-105-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-105">type(g) = generation</script> must hold.
-</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-106-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-106">Invalidated \subseteq Events \times Entities</script> saying when an event invalidated an entity.  An event can invalidate at most one entity, and if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-107-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-107">(evt,e)\in Invalidated</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-108-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-108">min(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-109-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-109">type(g) = invalidation</script> must hold.
-</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-110-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-110">EventActivity \subseteq Events \times Activities</script> associating activities with events, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-111-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-111">(act,evt) \in EventActivity</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-112-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-112">time(evt) \in lifetime(act)</script>.
-</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-113-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">⊆</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi mathvariant="normal">⊥</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-113">AssociatedWith \subseteq Association \times Agents \times Activities \times Plans_\bot</script> indicating when an agent is associated with an activity, and giving the identity of the association relationship, and an optional plan. 
-</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-114-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">⊆</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-114">ActsFor \subseteq Delegations \times Agents \times Agents \times Activities</script> indicating when one agent acts on behalf of another with respect to a given activity.  
+<ol><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-111-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-111">Used \subseteq Events \times Entities</script> saying when an event used an entity.  An event can use at most one entity, and if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-112-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-112">(evt,e)\in Used</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-113-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-113">time(evt) \in lifetime(e)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-114-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>u</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-114">type(evt) = usage</script> must hold.
+</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-115-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-115">Generated \subseteq Events \times Entities</script> saying when an event generated an entity.  An event can generate at most one entity, and if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-116-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-116">(evt,e)\in Generated</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-117-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-117">min(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-118-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-118">type(evt) = generation</script> must hold.
+</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-119-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-119">Invalidated \subseteq Events \times Entities</script> saying when an event invalidated an entity.  An event can invalidate at most one entity, and if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-120-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-120">(evt,e)\in Invalidated</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-121-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-121">max(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-122-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-122">type(evt) = invalidation</script> must hold.
+</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-123-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">⊆</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-123">EventActivity \subseteq Events \times Activities</script> associating activities with events, such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-124-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-124">(act,evt) \in EventActivity</script> implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-125-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-125">time(evt) \in lifetime(act)</script>.
+</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-126-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">⊆</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">×</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi mathvariant="normal">⊥</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-126">AssociatedWith \subseteq Associations \times Agents \times Activities \times Plans_\bot</script> indicating when an agent is associated with an activity, and giving the identity of the association relationship, and an optional plan. 
+</li><li> A relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-127-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi><mo stretchy="false">⊆</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">×</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-127">ActsFor \subseteq Delegations \times Agents \times Agents \times Activities</script> indicating when one agent acts on behalf of another with respect to a given activity.  
 </li></ol>
 
 <div class="note"><div class="note-title"><span>Note</span></div><div class="">
@@ -1459,6 +1547,11 @@
   TODO: Specialization relation
   </div></div>
 
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  EventActivity allows an event not to be associated with any
+  activity.  Is this OK?
+  </div></div>
+  
   <div class="note"><div class="note-title"><span>Note</span></div><div class="">
     TODO: Explicit axioms concerning the relations
   </div></div>
@@ -1469,48 +1562,68 @@
 
 <p>Recall that above we introduced a subset of interactions called <em>Derivations</em>.  These identify <em>paths</em> of the form </p>
 
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-115-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo stretchy="false">−</mo><mn>1</mn></mrow></msub><mo stretchy="false">⋅</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>0</mn></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-115">ent_n\cdot g_n\cdot  act_n\cdot  u_n\cdot  ent_{n-1}\cdot  ...\cdot
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-128-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mi>n</mi></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo stretchy="false">−</mo><mn>1</mn></mrow></msub><mo stretchy="false">⋅</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>0</mn></msub></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-128">ent_n\cdot g_n\cdot  act_n\cdot  u_n\cdot  ent_{n-1}\cdot  ...\cdot
 ent_1\cdot  g_1\cdot  act_1\cdot  u_1\cdot  ent_0</script>
 
-<p>where the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-116-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-116">ent_i</script> are entities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-117-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-117">act_i</script> are activities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-118-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-118">g_i</script> are generations, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-119-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-119">u_i</script> are usages.
+<p>where the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-129-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-129">ent_i</script> are entities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-130-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-130">act_i</script> are activities, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-131-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-131">g_i</script> are generations, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-132-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-132">u_i</script> are usages.
 </p>
 <p>Formally, we consider the (regular) language:
 </p>
-<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-120-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msup><mo stretchy="false">)</mo><mo stretchy="false">+</mo></msup></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-120">DerivationPaths = Entities \cdot (Events \cdot Activities \cdot
+<span class="MathJax_Preview"></span><div class="MathJax_MathML" id="MathJax-Element-133-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi><mo stretchy="false">=</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mo stretchy="false">(</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">⋅</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi><msup><mo stretchy="false">)</mo><mo stretchy="false">+</mo></msup></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-133">DerivationPaths = Entities \cdot (Events \cdot Activities \cdot
 Events \cdot Entities)^+</script>
 <p>with the constraints that for each derivation path:
 </p>
 <ul>
-<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-121-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-121">ent\cdot g \cdot act</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-122-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-122">(g,ent) \in Generated</script>  and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-123-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-123">(g,act) \in EventActivities</script>, and
+<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-134-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>g</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-134">ent\cdot g \cdot act</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-135-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-135">(g,ent) \in Generated</script>  and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-136-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-136">(g,act) \in EventActivity</script>, and
 </li>
-<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-124-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-124">act \cdot u \cdot ent</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-125-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-125">(u,ent) \in Used</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-126-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-126">(u,act) \in EventActivities</script>.
+<li>for each substring <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-137-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-137">act \cdot u \cdot ent</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-138-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-138">(u,ent) \in Used</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-139-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-139">(u,act) \in EventActivity</script>.
 </li>
 </ul>
-<p>We also consider a function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-127-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">:</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-127">derivedFrom : Derivations \to
-DerivationPaths</script>  linking each derivation to its path.</p>
-
-
-<div class="remark">The reason why we need paths and not just individual derivation steps is that imprecise wasDerivedFrom formulas can represent multiple derivation steps.</div>
+<p>Each derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-140-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-140">d \in Derivations</script> has an associated derivation path.  We link each derivation to an associated derivation path using the
+function <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-141-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">:</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-141">derivationPath : Derivations \to
+DerivationPaths</script>.  </p>
+
+<div class="remark">
+  <p>
+  The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-142-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-142">derivationPath</script> function links each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-143-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-143"> d \in Derivations</script> to a
+  derivation path.  A derivation has exactly one associated derivation
+  path.  However, if the PROV-N statement <span class="name">wasDerivedFrom(e_2,e_1,-,-,-)</span> is asserted in an
+  instance, there may be multiple derivation paths linking <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-144-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-144">e_2</script> to
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-145-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-145">e_1</script>, each corresponding to a different, identified by different
+  derivations <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-146-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-146">d \in Derivations</script>.
+  </p>
+  </div>
+
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  We can make the characterization of DerivationPaths more
+  precise/concise by introducing sets of Usage and Generation events.
+</div></div>
+
+<div class="remark">The reason why we need paths and not just individual derivation steps is that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-147-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-147">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> formulas can represent multiple derivation steps.</div>
 </section>
 </section>
 
 <section id="putting-it-all-together">
 <h3><span class="secno">3.4 </span> Putting it all together </h3>
 
-<p>A <em>structure</em> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-128-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-128">W</script> is a structure containing all of the above
+<p>A <em>structure</em> <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-148-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-148">W</script> is a structure containing all of the above
 described data.  If we need to talk about the objects or relations of
-more than one structure then we may write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-129-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-129">W_1.Objects</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-130-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-130">W_1.Things</script>,
+more than one structure then we may write <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-149-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-149">W_1.Objects</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-150-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mn>1</mn></msub><mo>.</mo><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-150">W_1.Things</script>,
 etc.; otherwise, to
 decrease notational clutter, when we consider a fixed structure then the names of the sets, relations and functions above refer to the components of that model.
 </p>
 
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  TODO: Highlight the distinctive vs obvious/routine features.
+  </div></div>
+
 </section>
 <section id="interpretations">
 <h3><span class="secno">3.5 </span> Interpretations </h3>
 
 <p>We need to link identifiers to the objects they denote.  We do this using a function which we shall call an <em>interpretation</em>.
  Thus, we consider interpretations as follows:
-An interpretation is a function  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-131-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">:</mo><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">→</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-131">\rho : Identifiers \to Objects</script> describing
+An interpretation is a function  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-151-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">:</mo><mi>I</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mi>s</mi><mo stretchy="false">→</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-151">\rho : Identifiers \to Objects</script> describing
 which object is the target of each identifier. The mapping from identifiers to objects may <b>not</b> change over time. 
 </p>
 </section>
@@ -1519,57 +1632,57 @@
 <section id="semantics">
 <!--OddPage--><h2><span class="secno">4. </span> Semantics </h2>
 
-<p>In what follows, let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-132-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-132">W</script> be a fixed structure with the associated sets and relations discussed in the previous section, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-133-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-133">I</script> be an interpretation of identifiers as objects in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-134-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-134">W</script>.
+<p>In what follows, let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-152-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-152">W</script> be a fixed structure with the associated sets and relations discussed in the previous section, and let <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-153-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-153">I</script> be an interpretation of identifiers as objects in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-154-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-154">W</script>.
 The annotations [WF] refer to well-formedness constraints that correspond to typing constraints.
 </p>
 
 <section id="satisfaction">
 <h3><span class="secno">4.1 </span> Satisfaction </h3>
 
-<p>Consider a formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-135-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-135">\phi</script>, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-136-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-136">W</script> and an interpretation
- <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-137-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-137">I</script>.
-We define notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-138-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-138">W,\rho \models \phi</script> which means that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-139-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-139">\phi</script> is
- satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-140-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-140">W,\rho</script>. For atomic formulas, the definition of the
+<p>Consider a formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-155-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-155">\phi</script>, a structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-156-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-156">W</script> and an interpretation
+ <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-157-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-157">I</script>.
+We define notation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-158-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-158">W,\rho \models \phi</script> which means that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-159-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-159">\phi</script> is
+ satisfied in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-160-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-160">W,\rho</script>. For atomic formulas, the definition of the
  satisfaction relation is given in the next few subsections.  We give
  the standard definition of the semantics of the other formulas:
 </p>
 
 <div class="formalism" id="first-order-logic" data-count="11" data-title="Formalism 11 (first-order-logic)"><div class="ruleTitle"><a class="internalDFN" href="#first-order-logic">Formalism 11 (first-order-logic)</a></div>
 <ol>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-141-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-141">W,\rho \models True</script> always holds.</li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-142-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-142">W,\rho \models False</script> never holds.</li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-143-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">¬</mi><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-143">W,\rho \models \neg \phi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-144-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-144">W,\rho \models
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-161-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>T</mi><mi>r</mi><mi>u</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-161">W,\rho \models True</script> always holds.</li>
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-162-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-162">W,\rho \models False</script> never holds.</li>
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-163-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">¬</mi><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-163">W,\rho \models \neg \phi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-164-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-164">W,\rho \models
   \phi</script> does not hold.</li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-145-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∧</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-145">W,\rho \models \phi \wedge \psi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-146-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-146">W,\rho \models
-  \phi</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-147-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi>i</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-147">W,i\models \psi</script>.</li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-148-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-148">W,\rho \models \phi \vee \psi</script> holds if either <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-149-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-149">W,\rho \models \phi</script>
-  or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-150-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-150">W,\rho \models \psi</script> holds.</li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-151-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">⇒</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-151">W,\rho \models \phi \Rightarrow \psi</script> holds if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-152-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-152">W,\rho \models \phi</script>
-  implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-153-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-153">W,\rho \models \psi</script>.</li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-154-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-154">W,\rho \models \exists x. \phi</script> holds if there exists some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-155-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-155">obj \in
-  Objects</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-156-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-156">W,\rho[x:=obj] \models \phi</script>.</li>
-  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-157-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-157">W,\rho \models \forall x. \phi</script> holds if there for every <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-158-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-158">obj \in
-  Objects</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-159-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-159">W,\rho[x:=obj] \models \phi</script>.</li>
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-165-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∧</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-165">W,\rho \models \phi \wedge \psi</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-166-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-166">W,\rho \models
+  \phi</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-167-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi>i</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-167">W,i\models \psi</script>.</li>
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-168-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">∨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-168">W,\rho \models \phi \vee \psi</script> holds if either <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-169-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-169">W,\rho \models \phi</script>
+  or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-170-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-170">W,\rho \models \psi</script> holds.</li>
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-171-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi><mo stretchy="false">⇒</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-171">W,\rho \models \phi \Rightarrow \psi</script> holds if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-172-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-172">W,\rho \models \phi</script>
+  implies <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-173-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="italic">ψ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-173">W,\rho \models \psi</script>.</li>
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-174-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∃</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-174">W,\rho \models \exists x. \phi</script> holds if there exists some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-175-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-175">obj \in
+  Objects</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-176-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-176">W,\rho[x:=obj] \models \phi</script>.</li>
+  <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-177-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo>.</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-177">W,\rho \models \forall x. \phi</script> holds if there for every <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-178-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">∈</mo><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-178">obj \in
+  Objects</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-179-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">[</mo><mi>x</mi><mo stretchy="false">:=</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">]</mo><mo stretchy="false">⊨</mo><mi mathvariant="italic">ϕ</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-179">W,\rho[x:=obj] \models \phi</script>.</li>
   </ol></div>
 
 <div class="remark">
   <p>In the semantics above, note that the domain of quantification is
-  the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-160-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-160">Objects</script>; that is, quantifiers range over entities,
+  the set of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-180-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-180">Objects</script>; that is, quantifiers range over entities,
   activities, agents, or interactions (which are in turn further
-  subdivided into types of interactions).  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-161-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-161">Things</script> and relations
+  subdivided into types of interactions).  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-181-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-181">Things</script> and relations
   cannot be referenced directly by identifiers.  
 </p>
   </div>
 
   <div class="remark">
-    <p>A PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-162-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-162">I</script> consists of a set of statements, each of
+    <p>A PROV instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-182-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-182">I</script> consists of a set of statements, each of
     which can be translated to an atomic formula following the
     definitional rules in PROV-CONSTRAINTS, possibly by introducing
     fresh existential variables.  Thus, we can view an
-    instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-163-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-163">I</script> as a set of atomic formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-164-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-164">\{\phi_1,\ldots,\phi_n\}</script>, or equivalently a
-    single formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-165-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∃</mi><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo>.</mo><mtext>&nbsp;</mtext><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-165">\exists x_1,\ldots,x_k.~\phi_1 \wedge \cdots
-    \wedge \phi_n</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-166-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-166">x_1,\ldots,x_k</script> are the existential
-    variables of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-167-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-167">I</script>.
+    instance <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-183-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-183">I</script> as a set of atomic formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-184-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-184">\{\phi_1,\ldots,\phi_n\}</script>, or equivalently a
+    single formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-185-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∃</mi><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub><mo>.</mo><mtext>&nbsp;</mtext><msub><mi mathvariant="italic">ϕ</mi><mn>1</mn></msub><mo stretchy="false">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</mo><msub><mi mathvariant="italic">ϕ</mi><mi>n</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-185">\exists x_1,\ldots,x_k.~\phi_1 \wedge \cdots
+    \wedge \phi_n</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-186-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>x</mi><mi>k</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-186">x_1,\ldots,x_k</script> are the existential
+    variables of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-187-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-187">I</script>.
     </p>
     </div>
 
@@ -1579,9 +1692,9 @@
 <h3><span class="secno">4.2 </span> Attribute matching </h3>
 
 
-<p>We say that an object <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-168-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-168">obj</script> matches attributes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-169-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>v</mi><mi>a</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">]</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-169">[attr_1=val_1,...]</script> in structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-170-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-170">W</script> provided:
-for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-171-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-171">attr_i</script>, we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-172-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><msub><mi>l</mi><mi>i</mi></msub><mo stretchy="false">∈</mo><mi>W</mi><mo>.</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-172">val_i \in W.value(obj,attr_i)</script>.
-This is sometimes abbreviated as: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-173-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-173">match(W,obj,attrs)</script>.
+<p>We say that an object <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-188-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-188">obj</script> matches attributes <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-189-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">[</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>v</mi><mi>a</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo stretchy="false">]</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-189">[attr_1=val_1,...]</script> in structure <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-190-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-190">W</script> provided:
+for each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-191-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-191">attr_i</script>, we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-192-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><msub><mi>l</mi><mi>i</mi></msub><mo stretchy="false">∈</mo><mi>W</mi><mo>.</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><msub><mi>r</mi><mi>i</mi></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-192">val_i \in W.value(obj,attr_i)</script>.
+This is sometimes abbreviated as: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-193-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>o</mi><mi>b</mi><mi>j</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-193">match(W,obj,attrs)</script>.
 </p>
     
 </section>
@@ -1593,23 +1706,24 @@
 
 <h4><span class="secno">4.3.1 </span> Entity </h4>
 
-<p>An entity formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-174-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-174">entity(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-175-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-175">id</script> denotes an entity.
+<p>An entity formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-194-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-194">entity(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-195-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-195">id</script> denotes an entity.
 </p>
-<p>Entity formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-176-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-176">entity(id,attrs)</script> can be interpreted as follows:
+<p>Entity formulas <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-196-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-196">entity(id,attrs)</script> can be interpreted as follows:
 </p>
 <div class="formalism" id="rule_12" data-count="12" data-title="Formalism 12 (rule_12)"><div class="ruleTitle"><a class="internalDFN" href="#rule_12">Formalism 12 (rule_12)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-177-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-177">W,\rho \models entity(id,attrs)</script> holds if and only if:</p>
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-197-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-197">W,\rho \models entity(id,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-178-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-178">id</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-179-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-179">ent = \rho(id) \in Entities</script>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-198-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-198">id</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-199-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-199">ent = \rho(id) \in Entities</script>
 </li>
-<li>the attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-180-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-180">match(W,ent, attrs)</script>.
+<li>the attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-200-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-200">match(W,ent, attrs)</script>.
 </li>
 </ol>
 
 
 </div>
 <div class="remark">
-<p>For example, the following formulas all hold if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-181-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-181">x</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-182-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-182">e</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-183-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>4</mn><mo stretchy="false">,</mo><mn>5</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">,</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-183">value(e,a) = \{4,5\}, value(e,b) = \{6\}</script> hold:
+<p>Not all of the attributes of an entity object are
+  required to be present in an entity formula about that object.  For example, the following formulas all hold if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-201-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-201">x</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-202-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-202">e</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-203-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>4</mn><mo stretchy="false">,</mo><mn>5</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">,</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-203">value(e,a) = \{4,5\}, value(e,b) = \{6\}</script> hold:
 </p><pre> entity(x,[])
  entity(x,[a=5])
  entity(x,[a=4,a=5])
@@ -1627,22 +1741,22 @@
 
 <h4><span class="secno">4.3.2 </span> Activity </h4>
 
-<p>An activity formula  is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-184-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-184">activity(id,st,et,attrs)</script>
-where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-185-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-185">id</script> is a identifier referring to the activity, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-186-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-186">st</script> is a start
-time and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-187-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-187">et</script> is an end time, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-188-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-188">attrs</script> are the attributes of
-activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-189-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-189">id</script>.
+<p>An activity formula  is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-204-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-204">activity(id,st,et,attrs)</script>
+where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-205-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-205">id</script> is a identifier referring to the activity, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-206-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-206">st</script> is a start
+time and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-207-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-207">et</script> is an end time, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-208-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-208">attrs</script> are the attributes of
+activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-209-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-209">id</script>.
 </p>
 <div class="formalism" id="rule_13" data-count="13" data-title="Formalism 13 (rule_13)"><div class="ruleTitle"><a class="internalDFN" href="#rule_13">Formalism 13 (rule_13)</a></div>
-  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-190-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-190">W,\rho \models activity(id,st,et,attrs)</script>
+  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-210-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-210">W,\rho \models activity(id,st,et,attrs)</script>
   holds if and only if:</p>
 <ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-191-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-191">id</script> maps to an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-192-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-192">act = \rho(id) \in Activities</script>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-211-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-211">id</script> maps to an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-212-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-212">act = \rho(id) \in Activities</script>
 </li>
-<li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-193-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-193">st</script> is specified then it is equal to the start time of the activity, that is: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-194-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-194">min(lifetime(id)) = st</script>
+<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-213-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-213">st</script> is the activity's start time, that is: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-214-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-214">min(lifetime(id)) = st</script>
 </li>
-<li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-195-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-195">et</script> is specified then it is equal to the end time of the activity, that is: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-196-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-196">max(lifetime(id)) = et</script>
+<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-215-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-215">et</script> is the activity's end time, that is: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-216-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-216">max(lifetime(id)) = et</script>
 </li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-197-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-197">match(W,act,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-217-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-217">match(W,act,attrs)</script>.
 </li>
 </ol>
 </div>
@@ -1651,15 +1765,15 @@
 
 <h4><span class="secno">4.3.3 </span> Agent </h4>
 
-<p>An agent formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-198-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-198">agent(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-199-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-199">id</script> denotes the agent and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-200-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-200">attrs</script> describes additional attributes.
+<p>An agent formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-218-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-218">agent(id,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-219-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-219">id</script> denotes the agent and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-220-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-220">attrs</script> describes additional attributes.
 </p>
 <div class="formalism" id="rule_14" data-count="14" data-title="Formalism 14 (rule_14)"><div class="ruleTitle"><a class="internalDFN" href="#rule_14">Formalism 14 (rule_14)</a></div>
-  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-201-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-201">W,\rho \models agent(id,attrs)</script> holds if and only if:
+  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-221-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-221">W,\rho \models agent(id,attrs)</script> holds if and only if:
   </p>
   <ol>
-    <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-202-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-202">id</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-203-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-203">ag = \rho(id) \in Agents</script>
+    <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-222-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-222">id</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-223-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-223">ag = \rho(id) \in Agents</script>
     </li>
-    <li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-204-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-204">match(W,ag,attrs)</script>.
+    <li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-224-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-224">match(W,ag,attrs)</script>.
     </li>
   </ol>
 </div>
@@ -1674,29 +1788,29 @@
 <h4><span class="secno">4.4.1 </span> Generation </h4>
 
 <p>The generation formula is of the form
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-205-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-205">wasGeneratedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-206-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-206">id</script> is an event identifier,
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-207-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-207">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-208-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-208">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-209-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-209">attrs</script> is
-a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-210-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-210">t</script> is a time.
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-225-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-225">wasGeneratedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-226-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-226">id</script> is an event identifier,
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-227-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-227">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-228-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-228">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-229-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-229">attrs</script> is
+a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-230-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-230">t</script> is a time.
 </p>
 <div class="formalism" id="rule_15" data-count="15" data-title="Formalism 15 (rule_15)"><div class="ruleTitle"><a class="internalDFN" href="#rule_15">Formalism 15 (rule_15)</a></div>
- <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-211-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-211">W,\rho \models
+ <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-231-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-231">W,\rho \models
   wasGeneratedBy(id,e,a,t,attrs)</script>  holds if and only if:
 </p><ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-212-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-212">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-213-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-213">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-214-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-214">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-215-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-215">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-216-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-216">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-217-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-217">act = \rho(a) \in Activities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-232-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-232">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-233-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-233">evt = \rho(id) \in Events</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-218-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-218">evt</script> is involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-219-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-219">act</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-220-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-220">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-221-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-221">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-222-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-222">generation</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-223-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-223">type(evt) = generation</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-234-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-234">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-235-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-235">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-224-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-224">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-225-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-225">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-226-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-226">time(evt) = t</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-236-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-236">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-237-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-237">act = \rho(a) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-227-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-227">evt</script> generated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-228-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-228">ent</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-229-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-229">(evt,ent) \in Generated</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-238-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-238">evt</script> is involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-239-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-239">act</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-240-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-240">(evt,act) \in EventActivity</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-230-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-230">match(W,evt,attrs)</script>.
+<li>The type of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-241-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-241">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-242-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-242">generation</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-243-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-243">type(evt) = generation</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-244-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-244">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-245-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-245">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-246-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-246">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-247-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-247">evt</script> generated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-248-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-248">ent</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-249-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-249">(evt,ent) \in Generated</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-250-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-250">match(W,evt,attrs)</script>.
 </li>
 </ol>
 </div>
@@ -1705,53 +1819,53 @@
 <section id="use">
 <h4><span class="secno">4.4.2 </span> Use </h4>
 
-<p>The use formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-231-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-231">used(id,a,e,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-232-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-232">id</script> denotes an event, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-233-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-233">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-234-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-234">e</script> is an object identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-235-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-235">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-236-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-236">t</script> is an optional time.
+<p>The use formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-251-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-251">used(id,a,e,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-252-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-252">id</script> denotes an event, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-253-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-253">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-254-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-254">e</script> is an object identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-255-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-255">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-256-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-256">t</script> is an optional time.
 </p>
 <div class="formalism" id="rule_16" data-count="16" data-title="Formalism 16 (rule_16)"><div class="ruleTitle"><a class="internalDFN" href="#rule_16">Formalism 16 (rule_16)</a></div>
-  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-237-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-237">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
+  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-257-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-257">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
   <ol>
 
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-238-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-238">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-239-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-239">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-240-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-240">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-241-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-241">act = \rho(id) \in Activities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-242-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-242">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-243-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-243">ent = \rho(e) \in Entities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-258-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-258">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-259-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-259">evt = \rho(id) \in Events</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-244-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-244">evt</script> is part of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-245-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-245">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-246-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-246">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-247-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-247">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-248-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-248">use</script>, i.e., <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-249-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>u</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-249">type(evt) = use</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-260-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-260">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-261-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-261">act = \rho(id) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-250-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-250">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-251-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-251">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-252-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-252">time(evt) = t</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-262-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-262">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-263-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-263">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-253-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-253">evt</script> used <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-254-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-254">obj</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-255-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-255">(evt,ent) \in Used</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-264-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-264">evt</script> is part of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-265-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-265">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-266-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-266">(evt,act) \in EventActivity</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-256-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-256">match(W,evt,attrs)</script>.
+<li>The type of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-267-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-267">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-268-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-268">use</script>, i.e., <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-269-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>u</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-269">type(evt) = use</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-270-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-270">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-271-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-271">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-272-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-272">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-273-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-273">evt</script> used <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-274-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><mi>j</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-274">obj</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-275-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>U</mi><mi>s</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-275">(evt,ent) \in Used</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-276-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-276">match(W,evt,attrs)</script>.
 </li></ol></div>
 
 </section>
 <section id="invalidation">
 <h4><span class="secno">4.4.3 </span> Invalidation </h4>
 
-<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-257-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-257">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-258-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-258">id</script> is an event identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-259-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-259">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-260-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-260">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-261-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-261">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-262-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-262">t</script> is an optional time.</p>
-
-<div class="formalism" id="rule_17" data-count="17" data-title="Formalism 17 (rule_17)"><div class="ruleTitle"><a class="internalDFN" href="#rule_17">Formalism 17 (rule_17)</a></div> <p>An invaliation formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-263-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-263">W,\rho \models
+<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-277-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-277">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-278-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-278">id</script> is an event identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-279-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-279">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-280-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-280">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-281-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-281">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-282-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-282">t</script> is an optional time.</p>
+
+<div class="formalism" id="rule_17" data-count="17" data-title="Formalism 17 (rule_17)"><div class="ruleTitle"><a class="internalDFN" href="#rule_17">Formalism 17 (rule_17)</a></div> <p>An invaliation formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-283-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-283">W,\rho \models
   wasInvalidatedBy(id,e,a,t,attrs)</script> holds  if and only if:</p>
 <ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-264-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-264">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-265-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-265">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-266-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-266">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-267-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-267">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-268-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-268">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-269-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-269">act = \rho(a) \in Activities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-284-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-284">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-285-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-285">evt = \rho(id) \in Events</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-270-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-270">evt</script> is involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-271-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-271">act</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-272-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-272">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-273-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-273">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-274-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-274">invalidation</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-275-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-275">type(evt) = invalidation</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-286-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-286">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-287-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-287">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-276-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-276">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-277-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-277">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-278-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-278">time(evt) = t</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-288-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-288">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-289-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-289">act = \rho(a) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-279-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-279">evt</script> invalidated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-280-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-280">ent</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-281-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-281">(evt,ent) \in Invalidated</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-290-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-290">evt</script> is involved in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-291-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-291">act</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-292-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-292">(evt,act) \in EventActivity</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-282-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-282">match(W,evt,attrs)</script>.
+<li>The type of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-293-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-293">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-294-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-294">invalidation</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-295-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-295">type(evt) = invalidation</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-296-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-296">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-297-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-297">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-298-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-298">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-299-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-299">evt</script> invalidated <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-300-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-300">ent</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-301-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-301">(evt,ent) \in Invalidated</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-302-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-302">match(W,evt,attrs)</script>.
 </li></ol></div>
 </section>
 
@@ -1759,74 +1873,88 @@
 
 <h4><span class="secno">4.4.4 </span> Association </h4>
 
-<p>An association formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-283-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-283">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
+<p>An association formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-303-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-303">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
 
 <div class="formalism" id="rule_18" data-count="18" data-title="Formalism 18 (rule_18)"><div class="ruleTitle"><a class="internalDFN" href="#rule_18">Formalism 18 (rule_18)</a></div><p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-284-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-284">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-304-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-304">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-285-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-285">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-286-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-286">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-287-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-287">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-288-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-288">act = \rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-305-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-305">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-306-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-306">assoc = \rho(id) \in Associations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-289-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-289">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-290-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-290">agent = \rho(ag) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-307-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-307">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-308-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-308">act = \rho(a) \in Activities</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-291-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-291">pl</script> is either the placeholder <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-292-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-292">-</script> or denotes a plan <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-293-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-293">plan=\rho(pl) \in Plans</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-309-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-309">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-310-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-310">agent = \rho(ag) \in Agents</script>.
 </li>
-<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-294-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-294">(assoc,agent,act,plan) \in AssociatedWith</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-311-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-311">pl</script> denotes a plan <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-312-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-312">plan=\rho(pl) \in Plans</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-295-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-295">match(W,assoc,attrs)</script>.
+<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-313-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mi>a</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-313">(assoc,agent,act,plan) \in AssociatedWith</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-314-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-314">match(W,assoc,attrs)</script>.
+</li></ol></div>
+
+<div class="formalism" id="rule_19" data-count="19" data-title="Formalism 19 (rule_19)"><div class="ruleTitle"><a class="internalDFN" href="#rule_19">Formalism 19 (rule_19)</a></div><p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-315-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-315">W,\rho \models wasAssociatedWith(id,a,ag,-,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-316-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-316">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-317-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-317">assoc = \rho(id) \in Associations</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-318-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-318">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-319-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-319">act = \rho(a) \in Activities</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-320-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-320">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-321-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-321">agent = \rho(ag) \in Agents</script>.
+</li>
+<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-322-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi mathvariant="normal">⊥</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-322">(assoc,agent,act,\bot) \in AssociatedWith</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-323-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-323">match(W,assoc,attrs)</script>.
 </li></ol></div>
 </section>
 <section id="start-formulas">
 <h4><span class="secno">4.4.5 </span> Start Formulas </h4>
 
-<p>A start formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-296-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-296">wasStartedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
-
-<div class="formalism" id="rule_19" data-count="19" data-title="Formalism 19 (rule_19)"><div class="ruleTitle"><a class="internalDFN" href="#rule_19">Formalism 19 (rule_19)</a></div>
-  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-297-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-297">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</script> holds if and only if:</p>
+<p>A start formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-324-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-324">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> is interpreted as follows:</p>
+
+<div class="formalism" id="rule_20" data-count="20" data-title="Formalism 20 (rule_20)"><div class="ruleTitle"><a class="internalDFN" href="#rule_20">Formalism 20 (rule_20)</a></div>
+  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-325-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-325">W,\rho \models wasStartedBy(id,a_2,e,a_1,t,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-298-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-298">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-299-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-299">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-300-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-300">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-301-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-301">act_2 = \rho(a_2) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-326-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-326">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-327-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-327">evt = \rho(id) \in Events</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-302-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-302">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-303-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-303">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-304-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-304">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-305-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-305">act_1 = \rho(a_1) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-328-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-328">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-329-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-329">act_2 = \rho(a_2) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-306-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-306">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-307-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-307">start</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-308-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-308">type(evt) = start</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-330-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-330">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-331-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-331">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event happened at the start of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-309-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-309">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-310-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-310">(evt,act_2)
-  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-311-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-311">min(lifetime(act_2)) = time(evt)</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-332-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-332">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-333-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-333">act_1 = \rho(a_1) \in Activities</script>.
 </li>
-<li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-312-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-312">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-313-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-313">act_1</script> and started <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-314-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-314">act_2</script>.
-</li><li>The event happened during <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-315-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-315">act_1</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-316-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-316">(evt,act_1)
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-334-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-334">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-335-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-335">start</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-336-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-336">type(evt) = start</script>.
+</li>
+<li>The event happened at the start of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-337-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-337">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-338-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-338">(evt,act_2)
+  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-339-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo stretchy="false">=</mo><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-339">t = min(lifetime(act_2)) = time(evt)</script>.
+</li>
+<li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-340-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-340">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-341-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-341">act_1</script> and started <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-342-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-342">act_2</script>.
+</li><li>The event happened during <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-343-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-343">act_1</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-344-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-344">(evt,act_1)
   \in EventsActivities</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-317-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-317">match(W,evt,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-345-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-345">match(W,evt,attrs)</script>.
 </li></ol></div>
 </section>
 <section id="end">
 <h4><span class="secno">4.4.6 </span> End </h4>
 
-<p>An activity end formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-318-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-318">wasEndedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
-
-<div class="formalism" id="rule_20" data-count="20" data-title="Formalism 20 (rule_20)"><div class="ruleTitle"><a class="internalDFN" href="#rule_20">Formalism 20 (rule_20)</a></div>
+<p>An activity end formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-346-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-346">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> is interpreted as follows:</p>
+
+<div class="formalism" id="rule_21" data-count="21" data-title="Formalism 21 (rule_21)"><div class="ruleTitle"><a class="internalDFN" href="#rule_21">Formalism 21 (rule_21)</a></div>
 <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-319-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-319">W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)</script> holds if and only
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-347-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-347">W,\rho \models wasEndedBy(id,a_2,e,a_1,t,attrs)</script> holds if and only
   if:</p>
   
 <ol>
-  <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-320-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-320">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-321-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-321">evt = \rho(id) \in Events</script>.</li>
-<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-322-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-322">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-323-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-323">act_2 = \rho(a_2)\in Activities</script>.</li>
-<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-324-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-324">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-325-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-325">ent = \rho(e)\in Entities</script>.</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-326-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-326">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-327-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-327">act_1 = \rho(a_1)\in Activities</script>.</li>
-<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-328-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-328">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-329-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-329">end</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-330-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-330">type(evt) = end</script>.</li>
-<li>The event happened at the end of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-331-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-331">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-332-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-332">(evt,act_2)
-  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-333-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-333">max(lifetime(act_2)) = time(evt)</script>.</li>
-  <li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-334-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-334">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-335-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-335">act_1</script> and ended <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-336-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-336">act_2</script>.</li>
-
-<li>The event happened during <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-337-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-337">act_1</script>, that is, $(evt,act_1) \in EventActivities.</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-338-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-338">match(W,evt,attrs)</script>.</li>
+  <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-348-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-348">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-349-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-349">evt = \rho(id) \in Events</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-350-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-350">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-351-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-351">act_2 = \rho(a_2)\in Activities</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-352-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-352">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-353-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-353">ent = \rho(e)\in Entities</script>.</li>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-354-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-354">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-355-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-355">act_1 = \rho(a_1)\in Activities</script>.</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-356-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>v</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-356">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-357-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-357">end</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-358-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-358">type(evt) = end</script>.</li>
+<li>The event happened at the end of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-359-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-359">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-360-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-360">(evt,act_2)
+  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-361-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo stretchy="false">=</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-361">t = max(lifetime(act_2)) = time(evt)</script>.</li>
+  <li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-362-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-362">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-363-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-363">act_1</script> and ended <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-364-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-364">act_2</script>.</li>
+
+<li>The event happened during <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-365-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-365">act_1</script>, that is, $(evt,act_1) \in EventActivity.</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-366-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-366">match(W,evt,attrs)</script>.</li>
 </ol>
 </div>
 </section>
@@ -1835,27 +1963,32 @@
 <h4><span class="secno">4.4.7 </span> Attribution </h4>
 
 <p>
-An attribution formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-339-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-339">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
+An attribution formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-367-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-367">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
 </p>
-<div class="formalism" id="rule_21" data-count="21" data-title="Formalism 21 (rule_21)"><div class="ruleTitle"><a class="internalDFN" href="#rule_21">Formalism 21 (rule_21)</a></div>
+<div class="formalism" id="rule_22" data-count="22" data-title="Formalism 22 (rule_22)"><div class="ruleTitle"><a class="internalDFN" href="#rule_22">Formalism 22 (rule_22)</a></div>
   <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-340-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-340">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-368-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-368">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
   holds if and only if:
   </p>
 <ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-341-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-341">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-342-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-342">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-343-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-343">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-344-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-344">ent = \rho(e) \in Entities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-369-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-369">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-370-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-370">assoc = \rho(id) \in Associations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-345-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-345">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-346-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-346">agent = \rho(ag) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-371-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-371">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-372-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-372">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-347-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-347">(assoc,ent,agent) \in AttributedTo</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-373-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-373">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-374-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-374">agent = \rho(ag) \in Agents</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-348-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-348">match(W,evt,attrs)</script>.
+<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-375-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-375">(assoc,ent,agent) \in AttributedTo</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-376-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>e</mi><mi>v</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-376">match(W,evt,attrs)</script>.
 </li></ol>
 </div>
 </section>
 
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+  TODO: Ensure that the semantics requires the agent's lifetime to
+  start before that of the entity.
+</div></div>
+
 <section id="communication">
 <h4><span class="secno">4.4.8 </span>Communication</h4>
 <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Communication</div></div>
@@ -1867,21 +2000,21 @@
 
 <h4><span class="secno">4.4.9 </span> Responsibility </h4>
 
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-349-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-349">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted using the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-350-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-350">ActsFor</script> relation as follows:</p>
-
-<div class="formalism" id="rule_22" data-count="22" data-title="Formalism 22 (rule_22)"><div class="ruleTitle"><a class="internalDFN" href="#rule_22">Formalism 22 (rule_22)</a></div>
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-377-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-377">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted using the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-378-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-378">ActsFor</script> relation as follows:</p>
+
+<div class="formalism" id="rule_23" data-count="23" data-title="Formalism 23 (rule_23)"><div class="ruleTitle"><a class="internalDFN" href="#rule_23">Formalism 23 (rule_23)</a></div>
   <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-351-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-351">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-379-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-379">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-352-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-352">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-353-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-353">deleg=\rho(id) \in Delegations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-354-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-354">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-355-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-355">act=\rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-380-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-380">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-381-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-381">deleg=\rho(id) \in Delegations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-356-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-356">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-357-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-357">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-382-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-382">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-383-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-383">act=\rho(a) \in Activities</script>.
 </li>
-<li>The agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-358-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-358">agent_2</script> acts for the agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-359-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-359">agent_1</script> with respect to the activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-360-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-360">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-361-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-361">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-384-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-384">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-385-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-385">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-362-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-362">match(W,assoc,attrs)</script>.
+<li>The agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-386-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-386">agent_2</script> acts for the agent <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-387-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-387">agent_1</script> with respect to the activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-388-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-388">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-389-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>e</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>s</mi><mi>F</mi><mi>o</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-389">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-390-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-390">match(W,assoc,attrs)</script>.
 </li></ol></div>
 </section>
 
@@ -1890,28 +2023,38 @@
 
 <h4><span class="secno">4.4.10 </span> Derivation </h4>
 
+<p>
+Derivation formulas can be of one of two forms:</p>
+<ul><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-391-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-391">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>, which specifies an
+  activity, generation and usage event.  For convenience we call
+  a <dfn id="dfn-precise-derivation">precise derivation</dfn>.</li>
+  <li> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-392-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-392">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>, which does not
+  specify an activity, generation and usage event.  For convenience we
+  call this an <dfn id="dfn-imprecise-derivation">imprecise derivation</dfn>.</li>
+  </ul>
+
 <section id="precise">
 <h5><span class="secno">4.4.10.1 </span> Precise </h5>
 
-<p>A precise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-363-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-363">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
+<p>A precise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-393-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-393">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
 </p>
-<div class="formalism" id="rule_23" data-count="23" data-title="Formalism 23 (rule_23)"><div class="ruleTitle"><a class="internalDFN" href="#rule_23">Formalism 23 (rule_23)</a></div>
-  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-364-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-364">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</script> holds if and only if:</p>
+<div class="formalism" id="rule_24" data-count="24" data-title="Formalism 24 (rule_24)"><div class="ruleTitle"><a class="internalDFN" href="#rule_24">Formalism 24 (rule_24)</a></div>
+  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-394-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-394">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-365-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-365">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-366-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-366">deriv = \rho(id) \in Derivations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-395-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-395">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-396-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-396">deriv = \rho(id) \in Derivations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-367-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-367">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-368-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-368">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> .
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-369-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-369">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-370-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-370">act = \rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-397-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-397">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-398-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-398">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> .
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-371-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-371">g</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-372-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-372">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-373-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-373">type(\rho(g)) = generation</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-399-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-399">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-400-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-400">act = \rho(a) \in Activities</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-374-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-374">u</script> denotes a use event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-375-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-375">\rho(u) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-376-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>u</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-376">type(\rho(u)) = use</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-401-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-401">g</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-402-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-402">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-403-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-403">type(\rho(g)) = generation</script>.
 </li>
-<li>The derivation denotes a one-step derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-377-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-377">derivedFrom(deriv) =
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-404-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-404">u</script> denotes a use event <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-405-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-405">\rho(u) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-406-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>u</mi><mi>s</mi><mi>e</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-406">type(\rho(u)) = use</script>.
+</li>
+<li>The derivation denotes a one-step derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-407-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⋅</mo><mi>a</mi><mi>c</mi><mi>t</mi><mo stretchy="false">⋅</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-407">derivationPath(deriv) =
 ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-378-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-378">match(W,deriv,attrs)</script>.</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-408-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-408">match(W,deriv,attrs)</script>.</li>
 </ol>
 </div>
 </section>
@@ -1919,18 +2062,18 @@
 
 <h5><span class="secno">4.4.10.2 </span> Imprecise </h5>
 <p>
-An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-379-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-379">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
-
-<div class="formalism" id="rule_24" data-count="24" data-title="Formalism 24 (rule_24)"><div class="ruleTitle"><a class="internalDFN" href="#rule_24">Formalism 24 (rule_24)</a></div>
-  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-380-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-380">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
+An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-409-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-409">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
+
+<div class="formalism" id="rule_25" data-count="25" data-title="Formalism 25 (rule_25)"><div class="ruleTitle"><a class="internalDFN" href="#rule_25">Formalism 25 (rule_25)</a></div>
+  <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-410-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-410">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-381-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-381">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-382-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-382">deriv = \rho(id) \in Derivations</script>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-411-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-411">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-412-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-412">deriv = \rho(id) \in Derivations</script>
 </li>
-<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-383-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-383">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-384-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-384">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> 
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-413-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-413">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-414-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-414">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> 
 </li>
-<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-385-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-385">derivedFrom(deriv)= ent_2 \cdot  w \cdot ent_1</script> for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-386-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-386">w</script>
+<li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-415-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">⋅</mo><mi>w</mi><mo stretchy="false">⋅</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-415">derivationPath(deriv)= ent_2 \cdot  w \cdot ent_1</script> for some <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-416-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-416">w</script>
 </li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-387-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-387">match(W,deriv,attrs)</script>.
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-417-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mi>t</mi><mi>c</mi><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mo stretchy="false">,</mo><mi>d</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-417">match(W,deriv,attrs)</script>.
 </li></ol></div>
 </section>
 </section>
@@ -1945,7 +2088,7 @@
 <section id="specialization">
 <h4><span class="secno">4.4.12 </span> Specialization </h4>
 
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-388-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-388">specializationOf(e_1,e_2)</script> relation indicates when one entity formula presents more specific aspects of another.  
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-418-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-418">specializationOf(e_1,e_2)</script> relation indicates when one entity formula presents more specific aspects of another.  
 </p>
   <div class="note"><div class="note-title"><span>Note</span></div><div class="">
     <p>TODO: The content of this definition may be moved into the
@@ -1953,26 +2096,26 @@
     itself this definition is not transitive.</p>
     </div></div>
     
-<div class="formalism" id="rule_25" data-count="25" data-title="Formalism 25 (rule_25)"><div class="ruleTitle"><a class="internalDFN" href="#rule_25">Formalism 25 (rule_25)</a></div>  <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-389-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-389">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
+<div class="formalism" id="rule_26" data-count="26" data-title="Formalism 26 (rule_26)"><div class="ruleTitle"><a class="internalDFN" href="#rule_26">Formalism 26 (rule_26)</a></div>  <p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-419-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-419">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-390-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-390">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-391-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-391">e_2</script> are entity identifiers, denoting
-  distinct entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-392-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-392">ent_1
-  = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-393-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-393">ent_2 = \rho(e_2) \in Entities</script>,
-  where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-394-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≠</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-394">ent_1 \neq ent_2</script>.
-</li>
-<li>The two Entities refer to the same Thing, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-395-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-395">thingOf(ent_1) = thingOf(ent_2)</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-420-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-420">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-421-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-421">e_2</script> are entity identifiers, denoting
+  distinct entities <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-422-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-422">ent_1
+  = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-423-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-423">ent_2 = \rho(e_2) \in Entities</script>,
+  where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-424-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">≠</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-424">ent_1 \neq ent_2</script>.
 </li>
-<li>The lifetime of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-396-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-396">obj_1</script> is contained in that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-397-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-397">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-398-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-398">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
+<li>The two Entities refer to the same Thing, that is, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-425-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-425">thingOf(ent_1) = thingOf(ent_2)</script>.
 </li>
-<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-399-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-399">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-400-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-400">value(obj_1,attr) \supseteq value(obj_2,attr)</script>.
+<li>The lifetime of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-426-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-426">ent_1</script> is contained in that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-427-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-427">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-428-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-428">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
+</li>
+<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-429-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-429">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-430-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-430">value(ent_1,attr) \supseteq value(ent_2,attr)</script>.
 </li></ol></div>
 
-<p>The second criterion says that the two Entities present aspects of
-the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-401-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-401">obj_1</script> and
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-402-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-402">obj_2</script> to have the same lifetime (or that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-403-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-403">obj_2</script> can be larger).
-The last criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-404-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-404">obj_1</script> to have more defined attributes than
-<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-405-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-405">obj_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-406-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-406">obj_2</script>.
+<p>The second criterion says that the two Entities present (possibly different) aspects of
+the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-431-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-431">ent_1</script> and
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-432-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-432">ent_2</script> to have the same lifetime (or that of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-433-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-433">ent_2</script> can be larger).
+The last criterion allows <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-434-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-434">ent_1</script> to have more defined attributes than
+<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-435-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-435">ent_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-436-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-436">ent_2</script>.
 </p>
 
 </section>
@@ -1980,15 +2123,15 @@
 
 <h4><span class="secno">4.4.13 </span> Alternate </h4>
 
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-407-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-407">alternateOf</script> relation indicates when two entity formulas present (possibly different) aspects of the same thing.  The two entities may or may not overlap in time.
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-437-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-437">alternateOf</script> relation indicates when two entity formulas present (possibly different) aspects of the same thing.  The two entities may or may not overlap in time.
 </p>
-<div class="formalism" id="rule_26" data-count="26" data-title="Formalism 26 (rule_26)"><div class="ruleTitle"><a class="internalDFN" href="#rule_26">Formalism 26 (rule_26)</a></div>
+<div class="formalism" id="rule_27" data-count="27" data-title="Formalism 27 (rule_27)"><div class="ruleTitle"><a class="internalDFN" href="#rule_27">Formalism 27 (rule_27)</a></div>
   <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-408-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-408">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-438-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-438">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-409-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-409">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-410-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-410">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-411-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-411">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-412-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-412">ent_2 = \rho(e_2)</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-439-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-439">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-440-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-440">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-441-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-441">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-442-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-442">ent_2 = \rho(e_2)</script>.
 </li>
-<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-413-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-413">thingOf(ent_1) = thingOf(ent_2)</script>
+<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-443-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-443">thingOf(ent_1) = thingOf(ent_2)</script>
 </li></ol>
 </div>
 
@@ -2000,14 +2143,14 @@
 
 <h4><span class="secno">4.4.14 </span> Membership </h4>
 
-<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-414-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-414">hadMember</script> relation relates a collection to an element of the collection.
+<p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-444-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-444">hadMember</script> relation relates a collection to an element of the collection.
 </p>
-<div class="formalism" id="rule_27" data-count="27" data-title="Formalism 27 (rule_27)"><div class="ruleTitle"><a class="internalDFN" href="#rule_27">Formalism 27 (rule_27)</a></div>
+<div class="formalism" id="rule_28" data-count="28" data-title="Formalism 28 (rule_28)"><div class="ruleTitle"><a class="internalDFN" href="#rule_28">Formalism 28 (rule_28)</a></div>
   <p>
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-415-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-415">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-445-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-445">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-416-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-416">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-417-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-417">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-418-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-418">coll
-  = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-419-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-419">ent = \rho(e) \in Entities</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-446-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-446">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-447-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-447">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-448-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>l</mi><mi>l</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-448">coll
+  = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-449-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-449">ent = \rho(e) \in Entities</script>.
 </li>
 <li>TODO
 </li></ol>
@@ -2032,38 +2175,54 @@
   <section id="equals">
   <h4><span class="secno">4.5.1 </span>Equals</h4>
   <p>As usual, an equality formula means that two expressions denote
-  the same value.  Identifiers always denote <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-420-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-420">Objects</script>.</p>
-  <div class="formalism" id="equality" data-count="28" data-title="Formalism 28 (equality)"><div class="ruleTitle"><a class="internalDFN" href="#equality">Formalism 28 (equality)</a></div>
-    <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-421-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">=</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-421">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-422-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-422">\rho(x) =
+  the same value.  Identifiers always denote <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-450-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>b</mi><mi>j</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-450">Objects</script>.</p>
+  <div class="formalism" id="equality" data-count="29" data-title="Formalism 29 (equality)"><div class="ruleTitle"><a class="internalDFN" href="#equality">Formalism 29 (equality)</a></div>
+    <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-451-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">=</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-451">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-452-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-452">\rho(x) =
     \rho(y)</script>.</p>
   </div>
   </section>
   <section id="precedes-and-strictly-precedes">
   <h4><span class="secno">4.5.2 </span>Precedes and Strictly Precedes</h4>
-  <p>The precedes relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-423-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-423">x \preceq y</script> holds between two events, one taking
+  <p>The precedes relation <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-453-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-453">x \preceq y</script> holds between two events, one taking
   place before (or simultaneously with) another.  Since the
-  reference semantics assumes that times are linearly ordered and
+naive semantics assumes that times are linearly ordered and
   event times are 
   mapped to a single time line, this amounts to
-  comparing the event times.  The semantics of strictly precedes (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-424-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-424">x
-  \prec y</script> is similar, only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-425-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-425">x</script> must take place strictly before <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-426-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-426">y</script>).</p>
-  <div class="formalism" id="precedes" data-count="29" data-title="Formalism 29 (precedes)"><div class="ruleTitle"><a class="internalDFN" href="#precedes">Formalism 29 (precedes)</a></div>
+  comparing the event times.  The semantics of strictly precedes (<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-454-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-454">x
+  \prec y</script> is similar, only <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-455-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-455">x</script> must take place strictly before <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-456-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-456">y</script>).</p>
+  <div class="formalism" id="precedes" data-count="30" data-title="Formalism 30 (precedes)"><div class="ruleTitle"><a class="internalDFN" href="#precedes">Formalism 30 (precedes)</a></div>
     <ol>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-427-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-427">W,\rho \models x \preceq y</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-428-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-428">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-429-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">≤</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-429">time(\rho(x)) \leq time(\rho(y))</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-430-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-430">W,\rho \models x \prec y</script> holds if and only if
-       <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-431-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-431">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-432-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">&lt;</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-432">time(\rho(x)) < time(\rho(y))</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-457-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">⪯</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-457">W,\rho \models x \preceq y</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-458-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-458">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-459-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">≤</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-459">time(\rho(x)) \leq time(\rho(y))</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-460-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>x</mi><mo stretchy="false">≺</mo><mi>y</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-460">W,\rho \models x \prec y</script> holds if and only if
+       <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-461-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>v</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-461">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-462-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">&lt;</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-462">time(\rho(x)) < time(\rho(y))</script>.</li>
     </ol>
   </div>
+
+  <div class="remark">
+    <p> Because we use a linearly ordered time to define event
+    precedence, there are valid PROV instances that are not satisfied
+    in any naive model.  For example:</p>
+    <pre>entity(e)
+activity(a1)
+activity(a2)
+wasGeneratedBy(gen1; e, a1, 2011-11-16T16:05:00)
+wasGeneratedBy(gen2; e, a2, 2012-11-16T16:05:00) //different date
+</pre>
+    <p>This instance is valid, and must satisfy precedence constraints
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-463-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-463">gen_1 \preceq gen_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-464-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-464">gen_2 \preceq gen_1</script>, but $time(gen_1)=
+    </p>
+    
+  </div>
   </section>
   
   <section id="notnull">
   <h4><span class="secno">4.5.3 </span>notNull</h4>
-  <p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-433-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-433">notNull(x)</script> formula is used to specify that a value may not
-  be the null value <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-434-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-434">\bot</script>.  The symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-435-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-435">-</script> always denotes the null
-  value (i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-436-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-436">\rho(-) = \bot</script>).
-  </p><div class="formalism" id="notNull" data-count="30" data-title="Formalism 30 (notNull)"><div class="ruleTitle"><a class="internalDFN" href="#notNull">Formalism 30 (notNull)</a></div>
-    <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-437-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-437">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-438-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">≠</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-438">e \neq
+  <p>The <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-465-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-465">notNull(x)</script> formula is used to specify that a value may not
+  be the null value <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-466-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-466">\bot</script>.  The symbol <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-467-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-467">-</script> always denotes the null
+  value (i.e. <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-468-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-468">\rho(-) = \bot</script>).
+  </p><div class="formalism" id="notNull" data-count="31" data-title="Formalism 31 (notNull)"><div class="ruleTitle"><a class="internalDFN" href="#notNull">Formalism 31 (notNull)</a></div>
+    <p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-469-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-469">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-470-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">≠</mo><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-470">e \neq
   \bot</script>.
       </p>
   </div> 
@@ -2073,19 +2232,19 @@
   <section id="typeof">
   <h4><span class="secno">4.5.4 </span>typeOf</h4>
   
-  <p>The typing formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-439-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-439">typeOf(x,t)</script> constrains the type of the value of
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-440-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-440">x</script>.  </p>
-
-  <div class="formalism" id="typeOf" data-count="31" data-title="Formalism 31 (typeOf)"><div class="ruleTitle"><a class="internalDFN" href="#typeOf">Formalism 31 (typeOf)</a></div>
-    <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-441-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-441">W,\rho\models typeOf(e,entity)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-442-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-442">\rho(e) \in Entities</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-443-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-443">W,\rho\models typeOf(a,activity)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-444-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-444">\rho(a) \in Activities</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-445-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-445">W,\rho\models typeOf(ag,agent)</script> holds if and only if
-      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-446-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-446">\rho(ag) \in Agents</script>.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-447-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-447">W,\rho\models typeOf(c,prov:Collection)</script> holds if and only if
+  <p>The typing formula <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-471-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-471">typeOf(x,t)</script> constrains the type of the value of
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-472-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-472">x</script>.  </p>
+
+  <div class="formalism" id="typeOf" data-count="32" data-title="Formalism 32 (typeOf)"><div class="ruleTitle"><a class="internalDFN" href="#typeOf">Formalism 32 (typeOf)</a></div>
+    <ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-473-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-473">W,\rho\models typeOf(e,entity)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-474-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-474">\rho(e) \in Entities</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-475-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-475">W,\rho\models typeOf(a,activity)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-476-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-476">\rho(a) \in Activities</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-477-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-477">W,\rho\models typeOf(ag,agent)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-478-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mi>A</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-478">\rho(ag) \in Agents</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-479-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-479">W,\rho\models typeOf(c,prov:Collection)</script> holds if and only if
       TODO.</li>
-      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-448-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-448">W,\rho\models typeOf(c,prov:EmptyCollection)</script> holds if and only if
+      <li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-480-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-480">W,\rho\models typeOf(c,prov:EmptyCollection)</script> holds if and only if
       TODO.</li>
       </ol>
       
@@ -2105,14 +2264,14 @@
     In this section we restate all of the inferences and constraints
     of PROV-CONSTRAINTS in terms of first-order logic.  For each, we
     give a proof sketch showing why the inference or constraint is
-    sound for reasoning about the reference semantics.  We exclude the
+    sound for reasoning about the naive semantics.  We exclude the
     definitional rules in PROV-CONSTRAINTS because they are only
     needed for expanding the abbreviated forms of PROV-N statements to
     the logical formulas used here.</p>
 <section id="inferences">
 <h3><span class="secno">5.1 </span>Inferences</h3>
 
-<div class="inference" id="communication-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#communication-generation-use-inference">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-449-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-449">\begin{array}[t]{l}
+<div class="inference" id="communication-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#communication-generation-use-inference">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-481-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>e</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-481">\begin{array}[t]{l}
 \forall id,a_2,a_1,attrs.~
 \\
 \qquad wasInformedBy(id,a_2,a_1,attrs)
@@ -2120,7 +2279,7 @@
 \quad\Rightarrow
 \exists e,gen,t_1,use,t_2.~wasGeneratedBy(gen,e,a_1,t_1,[]) \wedge used(use,a_2,e,t_2,[])
 \end{array}</script></div>
-<div class="inference" id="generation-use-communication-inference"><div class="ruleTitle"><a class="internalDFN" href="#generation-use-communication-inference">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-450-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-450">\begin{array}[t]{l}
+<div class="inference" id="generation-use-communication-inference"><div class="ruleTitle"><a class="internalDFN" href="#generation-use-communication-inference">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-482-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-482">\begin{array}[t]{l}
 \forall gen,e,a_1,t_1,attrs_1,id_2,a_2,t_2,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(id_2,a_2,e,t_2,attrs_2)
@@ -2128,7 +2287,7 @@
 \quad\Rightarrow
 \exists id.~wasInformedBy(id,a_2,a_1,[])
 \end{array}</script></div>
-<div class="inference" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a class="internalDFN" href="#entity-generation-invalidation-inference">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-451-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-451">\begin{array}[t]{l}
+<div class="inference" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a class="internalDFN" href="#entity-generation-invalidation-inference">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-483-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-483">\begin{array}[t]{l}
 \forall e,attrs.~
 \\
 \qquad entity(e,attrs)
@@ -2136,7 +2295,7 @@
 \quad\Rightarrow
 \exists gen,a_1,t_1,inv,a_2,t_2.~wasGeneratedBy(gen,e,a_1,t_1,[]) \wedge wasInvalidatedBy(inv,e,a_2,t_2,[])
 \end{array}</script></div>
-<div class="inference" id="activity-start-end-inference"><div class="ruleTitle"><a class="internalDFN" href="#activity-start-end-inference">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-452-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-452">\begin{array}[t]{l}
+<div class="inference" id="activity-start-end-inference"><div class="ruleTitle"><a class="internalDFN" href="#activity-start-end-inference">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-484-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-484">\begin{array}[t]{l}
 \forall a,t_1,t_2,attrs.~
 \\
 \qquad activity(a,t_1,t_2,attrs)
@@ -2144,7 +2303,7 @@
 \quad\Rightarrow
 \exists start,e_1,a_1,end,a_2,e_2.~wasStartedBy(start,a,e_1,a_1,t_1,[]) \wedge wasEndedBy(end,a,e_2,a_2,t_2,[])
 \end{array}</script></div>
-<div class="inference" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-453-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-453">\begin{array}[t]{l}
+<div class="inference" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-485-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-485">\begin{array}[t]{l}
 \forall id,a,e_1,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(id,a,e_1,a_1,t,attrs)
@@ -2152,7 +2311,7 @@
 \quad\Rightarrow
 \exists gen,t_1.~wasGeneratedBy(gen,e_1,a_1,t_1,[])
 \end{array}</script></div>
-<div class="inference" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-454-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-454">\begin{array}[t]{l}
+<div class="inference" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-486-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-486">\begin{array}[t]{l}
 \forall id,a,e_1,a_1,t,attrs.~
 \\
 \qquad wasEndedBy(id,a,e_1,a_1,t,attrs)
@@ -2160,7 +2319,7 @@
 \quad\Rightarrow
 \exists gen,t_1.~wasGeneratedBy(gen,e_1,a_1,t_1,[])
 \end{array}</script></div>
-<div class="inference" id="derivation-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-use-inference">Inference 11 (derivation-generation-use-inference)</a></div><p>In this inference, none of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-455-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-455">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-456-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-456">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-457-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-457">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-458-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-458">\begin{array}[t]{l}
+<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="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-487-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-487">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-488-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-488">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-489-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-489">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-490-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-490">\begin{array}[t]{l}
 \forall id,e_2,e_1,a,gen_2,use_1,attrs.~
 \\
 \qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(id,e_2,e_1,a,gen_2,use_1,attrs)
@@ -2168,7 +2327,7 @@
 \quad\Rightarrow
 \exists t_1,t_2.~used(use_1,a,e_1,t_1,[]) \wedge wasGeneratedBy(gen_2,e_2,a,t_2,[])
 \end{array}</script></div>
-<div class="inference" id="revision-is-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#revision-is-alternate-inference">Inference 12 (revision-is-alternate-inference)</a></div><p>In this inference, any of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-459-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-459">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-460-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-460">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-461-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-461">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-462-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-462">\begin{array}[t]{l}
+<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="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-491-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-491">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-492-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-492">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-493-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-493">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-494-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>R</mi><mi>e</mi><mi>v</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-494">\begin{array}[t]{l}
 \forall id,e_1,e_2,a,g,u.~
 \\
 \qquad wasDerivedFrom(id,e_2,e_1,a,g,u,[prov:type = prov:Revision]))
@@ -2176,7 +2335,7 @@
 \quad\Rightarrow
 alternateOf(e_2,e_1)
 \end{array}</script></div>
-<div class="inference" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-463-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-463">\begin{array}[t]{l}
+<div class="inference" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-495-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-495">\begin{array}[t]{l}
 \forall att,e,ag,attrs.~
 \\
 \qquad wasAttributedTo(att,e,ag,attrs)
@@ -2184,7 +2343,7 @@
 \quad\Rightarrow
 \exists a,t,gen,assoc,pl.~wasGeneratedBy(gen,e,a,t,[]) \wedge wasAssociatedWith(assoc,a,ag,pl,[])
 \end{array}</script></div>
-<div class="inference" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-464-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-464">\begin{array}[t]{l}
+<div class="inference" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-496-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi mathvariant="normal">∃</mi><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>p</mi><msub><mi>l</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-496">\begin{array}[t]{l}
 \forall id,ag_1,ag_2,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_1,ag_2,a,attrs)
@@ -2192,70 +2351,70 @@
 \quad\Rightarrow
 \exists id_1,pl_1,id_2,pl_2.~wasAssociatedWith(id_1,a,ag_1,pl_1,[]) \wedge wasAssociatedWith(id_2,a,ag_2,pl_2,[])
 \end{array}</script></div>
-<div class="inference" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-465-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-465">\begin{array}[t]{l}
+<div class="inference" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-497-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-497">\begin{array}[t]{l}
 \forall id,e,a,t,attrs.~
 \\
 \qquad wasGeneratedBy(id,e,a,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,e,a,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-466-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-466">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-498-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-498">\begin{array}[t]{l}
 \forall id,a,e,t,attrs.~
 \\
 \qquad used(id,a,e,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-467-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-467">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-499-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-499">\begin{array}[t]{l}
 \forall id,a_2,a_1,attrs.~
 \\
 \qquad wasInformedBy(id,a_2,a_1,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a_2,a_1,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-468-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-468">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-500-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-500">\begin{array}[t]{l}
 \forall id,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(id,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-469-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-469">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-501-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-501">\begin{array}[t]{l}
 \forall id,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasEndedBy(id,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-470-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-470">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-502-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-502">\begin{array}[t]{l}
 \forall id,e,a,t,attrs.~
 \\
 \qquad wasInvalidatedBy(id,e,a,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,e,a,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-471-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-471">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-503-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-503">\begin{array}[t]{l}
 \forall id,e_2,e_1,a,g,u,attrs.~
 \\
 \qquad wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,e_2,e_1,attrs)
-\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-472-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-472">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-473-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-473">g</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-474-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-474">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-475-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-475">\begin{array}[t]{l}
+\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-504-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-504">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-505-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-505">g</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-506-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-506">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-507-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-507">\begin{array}[t]{l}
 \forall id,e,ag,attrs.~
 \\
 \qquad wasAttributedTo(id,e,ag,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,e,ag,attrs)
-\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-476-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-476">pl</script> may be a placeholder -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-477-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-477">\begin{array}[t]{l}
+\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-508-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-508">pl</script> may be a placeholder -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-509-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-509">\begin{array}[t]{l}
 \forall id,a,ag,pl,attrs.~
 \\
 \qquad wasAssociatedWith(id,a,ag,pl,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,a,ag,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-478-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-478">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-510-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-510">\begin{array}[t]{l}
 \forall id,ag_2,ag_1,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
@@ -2263,7 +2422,7 @@
 \quad\Rightarrow
 wasInfluencedBy(id,ag_2,ag_1,attrs)
 \end{array}</script></li></ol></div>
-<div class="inference" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-479-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-479">\begin{array}[t]{l}
+<div class="inference" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-511-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-511">\begin{array}[t]{l}
 \forall e.~
 \\
 \qquad entity(e)
@@ -2272,10 +2431,10 @@
 alternateOf(e,e)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-480-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi>r</mi><mi>h</mi><mi>o</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-480">ent = rho(e)</script>.  Clearly <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-481-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-481">e \in Entities</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-482-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-482">thingOf(e) = thingOf(e)</script>, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-483-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-483">W,\rho \models alternateOf(e,e)</script>.</p>
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-512-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-512">ent = \rho(e)</script>.  Clearly <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-513-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo stretchy="false">∈</mo><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-513">e \in Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-514-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-514">thingOf(e) = thingOf(e)</script>, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-515-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-515">W,\rho \models alternateOf(e,e)</script>.</p>
   </div>
-<div class="inference" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-484-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-484">\begin{array}[t]{l}
+<div class="inference" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-516-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-516">\begin{array}[t]{l}
 \forall e_1,e_2,e_3.~
 \\
 \qquad alternateOf(e_1,e_2) \wedge alternateOf(e_2,e_3)
@@ -2284,13 +2443,13 @@
 alternateOf(e_1,e_3)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-485-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>r</mi><mi>h</mi><mi>o</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-485">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-486-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-486">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-487-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-487">ent_3 = \rho(e_3)</script>.  Then  by
-  assumption <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-488-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-488">ent_1</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-489-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-489">ent_2</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-490-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-490">ent_3</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-491-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-491">Entities</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-492-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-492">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-493-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-493">thingOf(e_2) = thingOf(e_3)</script>, so
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-494-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-494">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-495-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-495">W,\rho
-  \models alternateOf(e_2,e_1)</script>.</p>
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-517-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-517">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-518-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-518">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-519-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-519">ent_3 = \rho(e_3)</script>.  Then  by
+  assumption <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-520-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-520">ent_1</script>, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-521-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-521">ent_2</script>, and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-522-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-522">ent_3</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-523-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-523">Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-524-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-524">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-525-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-525">thingOf(e_2) = thingOf(e_3)</script>, so
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-526-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-526">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-527-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-527">W,\rho
+  \models alternateOf(e_1,e_3)</script>.</p>
   </div>
-<div class="inference" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-496-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-496">\begin{array}[t]{l}
+<div class="inference" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-528-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-528">\begin{array}[t]{l}
 \forall e_1,e_2.~
 \\
 \qquad alternateOf(e_1,e_2)
@@ -2299,13 +2458,13 @@
 alternateOf(e_2,e_1)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-497-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>r</mi><mi>h</mi><mi>o</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-497">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-498-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-498">ent_2 = \rho(e_2)</script>.  Then  by
-  assumption both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-499-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-499">ent_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-500-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-500">ent_2</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-501-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-501">Entities</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-502-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-502">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-503-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-503">W,\rho
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-529-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-529">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-530-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-530">ent_2 = \rho(e_2)</script>.  Then  by
+  assumption both <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-531-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-531">ent_1</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-532-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-532">ent_2</script> are in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-533-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-533">Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-534-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-534">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-535-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-535">W,\rho
   \models alternateOf(e_2,e_1)</script>.</p>
   </div>
   
-<div class="inference" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-504-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-504">\begin{array}[t]{l}
+<div class="inference" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-536-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-536">\begin{array}[t]{l}
 \forall e_1,e_2,e_3.~
 \\
 \qquad specializationOf(e_1,e_2) \wedge specializationOf(e_2,e_3)
@@ -2314,18 +2473,18 @@
 specializationOf(e_1,e_3)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-505-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-505">ent_1</script> and
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-506-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-506">ent_2</script> and for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-507-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-507">ent_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-508-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-508">ent_3</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-509-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-509">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-510-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-510">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-511-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-511">ent_3 =
-  \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-512-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-512">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
+  <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-537-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-537">ent_1</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-538-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-538">ent_2</script> and for <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-539-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-539">ent_2</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-540-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-540">ent_3</script>, where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-541-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-541">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-542-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-542">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-543-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>3</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-543">ent_3 =
+  \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-544-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">⊆</mo><mi>l</mi><mi>i</mi><mi>f</mi><mi>e</mi><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-544">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
   lifetime(e_3)</script>.  Moreover, 
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-513-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-513">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-514-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-514">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-515-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-515">value(obj_1,attr)
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-545-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-545">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-546-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-546">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-547-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>o</mi><mi>b</mi><msub><mi>j</mi><mn>3</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-547">value(obj_1,attr)
   \supseteq value(obj_3,attr)</script>.  (TODO:
-  How do we know <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-516-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">≠</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-516">e_3 \neq e_1</script>?  Need strict ordering on entities in semantics.)
+  How do we know <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-548-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>3</mn></msub><mo stretchy="false">≠</mo><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-548">e_3 \neq e_1</script>?  Need strict ordering on entities in semantics.)
 </p>
 </div>
 
-<div class="inference" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-517-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-517">\begin{array}[t]{l}
+<div class="inference" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-549-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-549">\begin{array}[t]{l}
 \forall e_1,e_2.~
 \\
 \qquad specializationOf(e_1,e_2)
@@ -2334,12 +2493,12 @@
 alternateOf(e_1,e_2)
 \end{array}</script></div>
 <div class="proof">
-  <p> If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-518-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-518">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-519-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-519">ent_2 = \rho(e_2)</script> are
-  specializations, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-520-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-520">thingOf(ent_1) = thingOf(ent_2)</script>.
+  <p> If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-550-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-550">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-551-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-551">ent_2 = \rho(e_2)</script> are
+  specializations, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-552-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-552">thingOf(ent_1) = thingOf(ent_2)</script>.
 </p>
 </div>
 
-<div class="inference" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-521-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-521">\begin{array}[t]{l}
+<div class="inference" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-553-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-553">\begin{array}[t]{l}
 \forall e_1,attrs,e_2.~
 \\
 \qquad entity(e_1,attrs) \wedge specializationOf(e_2,e_1)
@@ -2349,12 +2508,12 @@
 \end{array}</script></div>
 </section>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-522-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-522">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-523-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-523">ent_2 = \rho(e_2)</script>.  Suppose
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-524-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>v</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-524">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-525-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-525">attrs</script>.  Since
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-526-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-526">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-527-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-527">v \in value(ent_1,att)</script>.
-  Thus <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-528-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-528">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-529-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-529">value(ent_2,att) \supseteq value(ent_1,att)</script>.  Since
-  this is the case for all attribute-value pairs in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-530-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-530">attrs</script>, and since
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-531-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-531">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-532-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-532">W,\rho \models entity(e,attrs</script>).
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-554-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-554">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-555-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-555">ent_2 = \rho(e_2)</script>.  Suppose
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-556-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>v</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-556">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-557-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-557">attrs</script>.  Since
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-558-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-558">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-559-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-559">v \in value(ent_1,att)</script>.
+  Thus <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-560-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">∈</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-560">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-561-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">⊇</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-561">value(ent_2,att) \supseteq value(ent_1,att)</script>.  Since
+  this is the case for all attribute-value pairs in <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-562-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-562">attrs</script>, and since
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-563-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-563">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-564-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">,</mo><mi mathvariant="italic">ρ</mi><mo stretchy="false">⊨</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-564">W,\rho \models entity(e,attrs</script>).
   </p>
 </div>
 
@@ -2365,37 +2524,37 @@
 
 <div class="constraint" id="key-object"><div class="ruleTitle"><a class="internalDFN" href="#key-object">Constraint 22 (key-object)</a></div>
   <ol><li>The
-  identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-533-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-533">id</script> is a <span class="conditional">KEY</span> for
-  the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-534-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-534">entity(id,attrs)</script> statement.</li>
-  <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-535-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-535">id</script>
+  identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-565-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-565">id</script> is a <span class="conditional">KEY</span> for
+  the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-566-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-566">entity(id,attrs)</script> statement.</li>
+  <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-567-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-567">id</script>
   is a <span class="conditional">KEY</span> for the
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-536-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-536">activity(id,t_1,t_2,attrs)</script> statement.</li>
-  <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-537-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-537">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-538-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-538">agent(id,attrs)</script> statement.</li></ol></div>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-568-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-568">activity(id,t_1,t_2,attrs)</script> statement.</li>
+  <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-569-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-569">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-570-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-570">agent(id,attrs)</script> statement.</li></ol></div>
 <div class="constraint" id="key-properties"><div class="ruleTitle"><a class="internalDFN" href="#key-properties">Constraint 23 (key-properties)</a></div>
-  <ol><li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-539-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-539">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-540-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-540">wasGeneratedBy(id,e,a,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-541-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-541">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-542-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-542">used(id,a,e,t,attrs)</script>
+  <ol><li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-571-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-571">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-572-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-572">wasGeneratedBy(id,e,a,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-573-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-573">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-574-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-574">used(id,a,e,t,attrs)</script>
     statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-543-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-543">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-544-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-544">wasInformedBy(id,a_2,a_1,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-545-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-545">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-546-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-546">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-547-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-547">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-548-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-548">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-549-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-549">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-550-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-550">wasInvalidatedBy(id,e,a,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-551-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-551">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-552-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-552">wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-553-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-553">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-554-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-554">wasAttributedTo(id,e,ag,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-555-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-555">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-556-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-556">wasAssociatedWith(id,a,ag,pl,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-557-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-557">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-558-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-558">actedOnBehalfOf(id,ag_2,ag_1,a,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-559-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-559">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-560-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>o</mi><mn>2</mn><mo stretchy="false">,</mo><mi>o</mi><mn>1</mn><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-560">wasInfluencedBy(id,o2,o1,attrs)</script> statement.</li></ol>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-575-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-575">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-576-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-576">wasInformedBy(id,a_2,a_1,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-577-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-577">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-578-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-578">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-579-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-579">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-580-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-580">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-581-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-581">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-582-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-582">wasInvalidatedBy(id,e,a,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-583-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-583">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-584-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-584">wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-585-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-585">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-586-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-586">wasAttributedTo(id,e,ag,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-587-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-587">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-588-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-588">wasAssociatedWith(id,a,ag,pl,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-589-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-589">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-590-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-590">actedOnBehalfOf(id,ag_2,ag_1,a,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-591-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mi>d</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-591">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-592-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>l</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>o</mi><mn>2</mn><mo stretchy="false">,</mo><mi>o</mi><mn>1</mn><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-592">wasInfluencedBy(id,o2,o1,attrs)</script> statement.</li></ol>
   </div>
-<div class="constraint" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-561-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-561">\begin{array}[t]{l}
+<div class="constraint" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-593-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-593">\begin{array}[t]{l}
 \forall gen_1,gen_2,e,a,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen_1,e,a,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a,t_2,attrs_2)
@@ -2403,7 +2562,7 @@
 \quad\Rightarrow
 gen_1 = gen_2
 \end{array}</script></div>
-<div class="constraint" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-562-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-562">\begin{array}[t]{l}
+<div class="constraint" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-594-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-594">\begin{array}[t]{l}
 \forall inv_1,inv_2,e,a,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasInvalidatedBy(inv_1,e,a,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a,t_2,attrs_2)
@@ -2411,7 +2570,7 @@
 \quad\Rightarrow
 inv_1 = inv_2
 \end{array}</script></div>
-<div class="constraint" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-563-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-563">\begin{array}[t]{l}
+<div class="constraint" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-595-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-595">\begin{array}[t]{l}
 \forall start_1,start_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasStartedBy(start_1,a,e_1,a_0,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_0,t_2,attrs_2)
@@ -2419,7 +2578,7 @@
 \quad\Rightarrow
 start_1 = start_2
 \end{array}</script></div>
-<div class="constraint" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-564-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-564">\begin{array}[t]{l}
+<div class="constraint" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-596-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-596">\begin{array}[t]{l}
 \forall end_1,end_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasEndedBy(end_1,a,e_1,a_0,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_0,t_2,attrs_2)
@@ -2427,7 +2586,7 @@
 \quad\Rightarrow
 end_1 = end_2
 \end{array}</script></div>
-<div class="constraint" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-565-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-565">\begin{array}[t]{l}
+<div class="constraint" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-597-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-597">\begin{array}[t]{l}
 \forall start,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
 \\
 \qquad activity(a_2,t_1,t_2,attrs) \wedge wasStartedBy(start,a_2,e,a_1,t,attrs_1)
@@ -2435,7 +2594,7 @@
 \quad\Rightarrow
 t_1 = t
 \end{array}</script></div>
-<div class="constraint" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-566-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-566">\begin{array}[t]{l}
+<div class="constraint" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-598-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-598">\begin{array}[t]{l}
 \forall end,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
 \\
 \qquad activity(a_2,t_1,t_2,attrs) \wedge wasEndedBy(end,a_2,e,a_1,t,attrs_1)
@@ -2449,7 +2608,7 @@
 <h4><span class="secno">5.2.2 </span>Ordering constraints</h4>
 
 
-<div class="constraint" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-567-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-567">\begin{array}[t]{l}
+<div class="constraint" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-599-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-599">\begin{array}[t]{l}
 \forall start,end,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
@@ -2457,7 +2616,7 @@
 \quad\Rightarrow
 start \preceq end
 \end{array}</script></div>
-<div class="constraint" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-568-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-568">\begin{array}[t]{l}
+<div class="constraint" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-600-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-600">\begin{array}[t]{l}
 \forall start_1,start_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_2,t_2,attrs_2)
@@ -2465,7 +2624,7 @@
 \quad\Rightarrow
 start_1 \preceq start_2
 \end{array}</script></div>
-<div class="constraint" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-569-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-569">\begin{array}[t]{l}
+<div class="constraint" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-601-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-601">\begin{array}[t]{l}
 \forall end_1,end_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasEndedBy(end_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
@@ -2473,14 +2632,14 @@
 \quad\Rightarrow
 end_1 \preceq end_2
 \end{array}</script></div>
-<div class="constraint" id="usage-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#usage-within-activity">Constraint 33 (usage-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-570-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-570">\begin{array}[t]{l}
+<div class="constraint" id="usage-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#usage-within-activity">Constraint 33 (usage-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-602-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-602">\begin{array}[t]{l}
 \forall start,use,a,e_1,e_2,a_1,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge used(use,a,e_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 start \preceq use
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-571-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-571">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-603-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-603">\begin{array}[t]{l}
 \forall use,end,a,e_1,e_2,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad used(use,a,e_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
@@ -2488,14 +2647,14 @@
 \quad\Rightarrow
 use \preceq end
 \end{array}</script></li></ol></div>
-<div class="constraint" id="generation-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#generation-within-activity">Constraint 34 (generation-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-572-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-572">\begin{array}[t]{l}
+<div class="constraint" id="generation-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#generation-within-activity">Constraint 34 (generation-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-604-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><mi>n</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-604">\begin{array}[t]{l}
 \forall start,gen,e_1,e_2,a,a_1,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen,e_2,a,t_2,attrs_2)
 \\
 \quad\Rightarrow
 start \preceq gen
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-573-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-573">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-605-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-605">\begin{array}[t]{l}
 \forall gen,end,e,e_1,a,a_1,t,t_1,attrs,attrs_1.~
 \\
 \qquad wasGeneratedBy(gen,e,a,t,attrs) \wedge wasEndedBy(end,a,e_1,a_1,t_1,attrs_1)
@@ -2503,7 +2662,7 @@
 \quad\Rightarrow
 gen \preceq end
 \end{array}</script></li></ol></div>
-<div class="constraint" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-574-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-574">\begin{array}[t]{l}
+<div class="constraint" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-606-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msubsup><mi>a</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-606">\begin{array}[t]{l}
 \forall id,start,end,a_1,a_1',a_2,a_2',e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
 \\
 \qquad wasInformedBy(id,a_2,a_1,attrs) \wedge wasStartedBy(start,a_1,e_1,a_1',t_1,attrs_1) \wedge wasEndedBy(end,a_2,e_2,a_2',t_2,attrs_2)
@@ -2511,7 +2670,7 @@
 \quad\Rightarrow
 start \preceq end
 \end{array}</script></div>
-<div class="constraint" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-575-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-575">\begin{array}[t]{l}
+<div class="constraint" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-607-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-607">\begin{array}[t]{l}
 \forall gen,inv,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -2519,7 +2678,7 @@
 \quad\Rightarrow
 gen \preceq inv
 \end{array}</script></div>
-<div class="constraint" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-576-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-576">\begin{array}[t]{l}
+<div class="constraint" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-608-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>u</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-608">\begin{array}[t]{l}
 \forall gen,use,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(use,a_2,e,t_2,attrs_2)
@@ -2527,7 +2686,7 @@
 \quad\Rightarrow
 gen \preceq use
 \end{array}</script></div>
-<div class="constraint" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-577-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-577">\begin{array}[t]{l}
+<div class="constraint" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-609-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><mi>e</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-609">\begin{array}[t]{l}
 \forall use,inv,a_1,a_2,e,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad used(use,a_1,e,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -2535,7 +2694,7 @@
 \quad\Rightarrow
 use \preceq inv
 \end{array}</script></div>
-<div class="constraint" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-578-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-578">\begin{array}[t]{l}
+<div class="constraint" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-610-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-610">\begin{array}[t]{l}
 \forall gen_1,gen_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen_1,e,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
@@ -2543,7 +2702,7 @@
 \quad\Rightarrow
 gen_1 \preceq gen_2
 \end{array}</script></div>
-<div class="constraint" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-579-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-579">\begin{array}[t]{l}
+<div class="constraint" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-611-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-611">\begin{array}[t]{l}
 \forall inv_1,inv_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasInvalidatedBy(inv_1,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a_2,t_2,attrs_2)
@@ -2551,7 +2710,7 @@
 \quad\Rightarrow
 inv_1 \preceq inv_2
 \end{array}</script></div>
-<div class="constraint" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><p>In this constraint, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-580-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-580">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-581-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-581">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-582-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-582">use_1</script> must not be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-583-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-583">\begin{array}[t]{l}
+<div class="constraint" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><p>In this constraint, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-612-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-612">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-613-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-613">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-614-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub></math></span></span></span><script type="math/tex" id="MathJax-Element-614">use_1</script> must not be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-615-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>u</mi><mi>s</mi><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-615">\begin{array}[t]{l}
 \forall d,e_1,e_2,a,gen_2,use_1,attrs.~
 \\
 \qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(d,e_2,e_1,a,gen_2,use_1,attrs)
@@ -2559,7 +2718,7 @@
 \quad\Rightarrow
 use_1 \preceq gen_2
 \end{array}</script></div>
-<div class="constraint" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><p>In this constraint, any of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-584-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-584">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-585-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-585">g</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-586-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-586">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-587-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">≺</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-587">\begin{array}[t]{l}
+<div class="constraint" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><p>In this constraint, any of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-616-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-616">a</script>,<span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-617-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-617">g</script>, or <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-618-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-618">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-619-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">≺</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-619">\begin{array}[t]{l}
 \forall d,gen_1,gen_2,e_1,e_2,a,a_1,a_2,g,u,t_1,t_2,attrs,attrs_1,attrs_2.~
 \\
 \qquad wasDerivedFrom(d,e_2,e_1,a,g,u,attrs) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
@@ -2567,14 +2726,14 @@
 \quad\Rightarrow
 gen_1 \prec gen_2
 \end{array}</script></div>
-<div class="constraint" id="wasStartedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-ordering">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-588-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-588">\begin{array}[t]{l}
+<div class="constraint" id="wasStartedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-ordering">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-620-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-620">\begin{array}[t]{l}
 \forall gen,start,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasStartedBy(start,a,e,a_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 gen \preceq start
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-589-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-589">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-621-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-621">\begin{array}[t]{l}
 \forall start,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasStartedBy(start,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -2582,14 +2741,14 @@
 \quad\Rightarrow
 start \preceq inv
 \end{array}</script></li></ol></div>
-<div class="constraint" id="wasEndedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-ordering">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-590-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-590">\begin{array}[t]{l}
+<div class="constraint" id="wasEndedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-ordering">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-622-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><mi>n</mi><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><mi>d</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-622">\begin{array}[t]{l}
 \forall gen,end,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e,a_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 gen \preceq end
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-591-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-591">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-623-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><mi>v</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-623">\begin{array}[t]{l}
 \forall end,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasEndedBy(end,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
@@ -2597,7 +2756,7 @@
 \quad\Rightarrow
 end \preceq inv
 \end{array}</script></li></ol></div>
-<div class="constraint" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-592-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-592">\begin{array}[t]{l}
+<div class="constraint" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-624-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-624">\begin{array}[t]{l}
 \forall gen_1,gen_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad specializationOf(e_2,e_1) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
@@ -2605,7 +2764,7 @@
 \quad\Rightarrow
 gen_1 \preceq gen_2
 \end{array}</script></div>
-<div class="constraint" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-593-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-593">\begin{array}[t]{l}
+<div class="constraint" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-625-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-625">\begin{array}[t]{l}
 \forall inv_1,inv_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad specializationOf(e_1,e_2) \wedge wasInvalidatedBy(inv_1,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e_2,a_2,t_2,attrs_2)
@@ -2613,28 +2772,28 @@
 \quad\Rightarrow
 inv_1 \preceq inv_2
 \end{array}</script></div>
-<div class="constraint" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAssociatedWith-ordering">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-594-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-594">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-595-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-595">\begin{array}[t]{l}
+<div class="constraint" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAssociatedWith-ordering">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-626-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>l</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-626">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-627-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-627">\begin{array}[t]{l}
 \forall assoc,start_1,inv_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag,a_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 start_1 \preceq inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-596-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-596">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-628-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-628">\begin{array}[t]{l}
 \forall assoc,gen_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 gen_1 \preceq end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-597-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-597">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-629-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-629">\begin{array}[t]{l}
 \forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag,e_2,a_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 start_1 \preceq end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-598-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-598">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-630-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>a</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-630">\begin{array}[t]{l}
 \forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
 \\
 \qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
@@ -2642,14 +2801,14 @@
 \quad\Rightarrow
 start_1 \preceq end_2
 \end{array}</script></li></ol></div>
-<div class="constraint" id="wasAttributedTo-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAttributedTo-ordering">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-599-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-599">\begin{array}[t]{l}
+<div class="constraint" id="wasAttributedTo-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAttributedTo-ordering">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-631-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-631">\begin{array}[t]{l}
 \forall att,gen_1,gen_2,e,a_1,a_2,t_1,t_2,ag,attrs,attrs_1,attrs_2.~
 \\
 \qquad wasAttributedTo(att,e,ag,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 gen_1 \preceq gen_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-600-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-600">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-632-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mi>t</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-632">\begin{array}[t]{l}
 \forall att,start_1,gen_2,e,e_1,a_1,a_2,ag,t_1,t_2,attrs,attrs_1,attrs_2.~
 \\
 \qquad wasAttributedTo(att,e,ag,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
@@ -2657,14 +2816,14 @@
 \quad\Rightarrow
 start_1 \preceq gen_2
 \end{array}</script></li></ol></div>
-<div class="constraint" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a class="internalDFN" href="#actedOnBehalfOf-ordering">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-601-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-601">\begin{array}[t]{l}
+<div class="constraint" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a class="internalDFN" href="#actedOnBehalfOf-ordering">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-633-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>g</mi><mi>e</mi><msub><mi>n</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>i</mi><mi>n</mi><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-633">\begin{array}[t]{l}
 \forall del,gen_1,inv_2,ag_1,ag_2,a,a_1,a_2,t_1,t_2,attrs,attrs_1,attrs_2.~
 \\
 \qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasGeneratedBy(gen_1,ag_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag_2,a_2,t_2,attrs_2)
 \\
 \quad\Rightarrow
 gen_1 \preceq inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-602-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-602">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-634-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>d</mi><mi>e</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><msub><mi>s</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">⪯</mo><mi>e</mi><mi>n</mi><msub><mi>d</mi><mn>2</mn></msub></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-634">\begin{array}[t]{l}
 \forall del,start_1,end_2,ag_1,ag_2,a,a_1,a_2,e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
 \\
 \qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasStartedBy(start_1,ag_1,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag_2,e_2,a_2,t_2,attrs_2)
@@ -2678,133 +2837,133 @@
 <section id="typing-constraints">
 <h4><span class="secno">5.2.3 </span>Typing constraints</h4>
 
-<div class="constraint" id="typing"><div class="ruleTitle"><a class="internalDFN" href="#typing">Constraint 50 (typing)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-603-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-603">\begin{array}[t]{l}
+<div class="constraint" id="typing"><div class="ruleTitle"><a class="internalDFN" href="#typing">Constraint 50 (typing)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-635-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-635">\begin{array}[t]{l}
 \forall e,attrs.~
 \\
 \qquad entity(e,attrs)
 \\
 \quad\Rightarrow
 typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-604-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-604">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-636-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-636">\begin{array}[t]{l}
 \forall ag,attrs.~
 \\
 \qquad agent(ag,attrs)
 \\
 \quad\Rightarrow
 typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-605-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-605">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-637-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-637">\begin{array}[t]{l}
 \forall a,t_1,t_2,attrs.~
 \\
 \qquad activity(a,t_1,t_2,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-606-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-606">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-638-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-638">\begin{array}[t]{l}
 \forall u,a,e,t,attrs.~
 \\
 \qquad used(u,a,e,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-607-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-607">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-639-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-639">\begin{array}[t]{l}
 \forall g,a,e,t,attrs.~
 \\
 \qquad wasGeneratedBy(g,e,a,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-608-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-608">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-640-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>f</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-640">\begin{array}[t]{l}
 \forall inf,a_2,a_1,t,attrs.~
 \\
 \qquad wasInformedBy(inf,a_2,a_1,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a_1,activity) \wedge typeOf(a_2,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-609-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-609">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-641-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>s</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-641">\begin{array}[t]{l}
 \forall start,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(start,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-610-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-610">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-642-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>e</mi><mi>n</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-642">\begin{array}[t]{l}
 \forall end,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasEndedBy(end,a_2,e,a_1,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-611-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-611">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-643-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mi>v</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>t</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-643">\begin{array}[t]{l}
 \forall inv,a,e,t,attrs.~
 \\
 \qquad wasInvalidatedBy(inv,e,a,t,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-612-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-612">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-644-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>u</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-644">\begin{array}[t]{l}
 \forall id,e_2,e_1,a,g_2,u_1,attrs.~
 \\
 \qquad notNull(a) \wedge notNull(g_2) \wedge notNull(u_1) \wedge wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,activity) \wedge typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-613-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-613">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-645-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-645">\begin{array}[t]{l}
 \forall id,e_2,e_1,attrs.~
 \\
 \qquad wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-614-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-614">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-646-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-646">\begin{array}[t]{l}
 \forall id,e,ag,attrs.~
 \\
 \qquad wasAttributedTo(id,e,ag,attrs)
 \\
 \quad\Rightarrow
 typeOf(e,entity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-615-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-615">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-647-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>p</mi><mi>l</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-647">\begin{array}[t]{l}
 \forall id,a,ag,pl,attrs.~
 \\
 \qquad notNull(pl) \wedge wasAssociatedWith(id,a,ag,pl,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(ag,agent) \wedge typeOf(pl,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-616-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-616">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-648-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-648">\begin{array}[t]{l}
 \forall id,a,ag,attrs.~
 \\
 \qquad wasAssociatedWith(id,a,ag,-,attrs)
 \\
 \quad\Rightarrow
 typeOf(a,activity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-617-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-617">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-649-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><msub><mi>g</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-649">\begin{array}[t]{l}
 \forall id,ag_2,ag_1,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
 \\
 \quad\Rightarrow
 typeOf(ag_2,agent) \wedge typeOf(ag_1,agent) \wedge typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-618-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-618">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-650-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>a</mi><mi>l</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-650">\begin{array}[t]{l}
 \forall e_2,e_1.~
 \\
 \qquad alternateOf(e_2,e_1)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-619-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-619">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-651-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-651">\begin{array}[t]{l}
 \forall e_2,e_1.~
 \\
 \qquad specializationOf(e_2,e_1)
 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-620-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-620">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-652-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>d</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-652">\begin{array}[t]{l}
 \forall c,e.~
 \\
 \qquad hadMember(c,e)
 \\
 \quad\Rightarrow
 typeOf(c,prov:Collection) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-621-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-621">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-653-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mo stretchy="false">[</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo stretchy="false">=</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>e</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-653">\begin{array}[t]{l}
 \forall c.~
 \\
 \qquad entity(c,[prov:type = prov:emptyCollection]))
@@ -2822,21 +2981,21 @@
 <section id="impossibility-constraints">
 <h4><span class="secno">5.2.4 </span>Impossibility constraints</h4>
 
-<div class="constraint" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a class="internalDFN" href="#impossible-unspecified-derivation-generation-use">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-622-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-622">\begin{array}[t]{l}
+<div class="constraint" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a class="internalDFN" href="#impossible-unspecified-derivation-generation-use">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-654-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-654">\begin{array}[t]{l}
 \forall id,e_1,e_2,g,attrs.~
 \\
 \qquad notNull(g) \wedge wasDerivedFrom(id,e_2,e_1,-,g,-,attrs)
 \\
 \quad\Rightarrow
 False
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-623-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-623">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-655-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-655">\begin{array}[t]{l}
 \forall id,e_1,e_2,u,attrs.~
 \\
 \qquad notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,-,u,attrs)
 \\
 \quad\Rightarrow
 False
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-624-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-624">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-656-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>n</mi><mi>o</mi><mi>t</mi><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>e</mi><mn>2</mn></msub><mo stretchy="false">,</mo><msub><mi>e</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">−</mo><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi><mo stretchy="false">,</mo><mi>a</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>s</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-656">\begin{array}[t]{l}
 \forall id,e_1,e_2,g,u,attrs.~
 \\
 \qquad notNull(g) \wedge notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,g,u,attrs)
@@ -2846,10 +3005,10 @@
 \end{array}</script></li></ol></div>
 <div class="proof">
   <p>Each part follows from the fact that the semantics of
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-625-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-625">wasDerivedFrom</script> only allows formulas to hold when either all three
-  of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-626-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-626">a,g,u</script> are <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-627-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-627">-</script> (denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-628-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-628">\bot</script>) or none of them are.</p>
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-657-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mi>a</mi><mi>s</mi><mi>D</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>v</mi><mi>e</mi><mi>d</mi><mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-657">wasDerivedFrom</script> only allows formulas to hold when either all three
+  of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-658-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo stretchy="false">,</mo><mi>g</mi><mo stretchy="false">,</mo><mi>u</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-658">a,g,u</script> are <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-659-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">−</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-659">-</script> (denoting <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-660-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">⊥</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-660">\bot</script>) or none of them are.</p>
   </div>
-<div class="constraint" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-629-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-629">\begin{array}[t]{l}
+<div class="constraint" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-661-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>e</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-661">\begin{array}[t]{l}
 \forall e.~
 \\
 \qquad specializationOf(e,e)
@@ -2859,11 +3018,11 @@
 \end{array}</script></div>
 <div class="proof">
   <p>This follows from the fact that in the semantics of
-  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-630-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-630">specializationOf</script>, the two entities denoted by the first and second
+  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-662-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>O</mi><mi>f</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-662">specializationOf</script>, the two entities denoted by the first and second
   arguments are required to be distinct.
   </p>
   </div>
-<div class="constraint" id="impossible-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-property-overlap">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-631-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-631">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-632-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-632">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-633-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-633">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-634-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-634">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-635-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-635">\begin{array}[t]{l}
+<div class="constraint" id="impossible-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-property-overlap">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-663-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-663">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-664-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-664">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-665-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-665">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-666-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-666">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-667-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>s</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-667">\begin{array}[t]{l}
 \forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
 \\
 \qquad r(id,a_1,\ldots,a_m) \wedge s(id,b_1,\ldots,b_n)
@@ -2876,7 +3035,7 @@
   interactions are disjoint sets, characterized by their types.
   </p>
   </div>
-<div class="constraint" id="impossible-object-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-object-property-overlap">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-636-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-636">p \in \{entity,activity,agent\}</script>  and each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-637-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-637">r \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script>, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-638-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>p</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-638">\begin{array}[t]{l}
+<div class="constraint" id="impossible-object-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-object-property-overlap">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-668-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">,</mo><mi>a</mi><mi>g</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-668">p \in \{entity,activity,agent\}</script>  and each <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-669-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>d</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>G</mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>v</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>S</mi><mi>t</mi><mi>a</mi><mi>r</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>E</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>I</mi><mi>n</mi><mi>f</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>e</mi><mi>d</mi><mi>B</mi><mi>y</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>t</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>b</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>o</mi><mo stretchy="false">,</mo><mi>w</mi><mi>a</mi><mi>s</mi><mi>A</mi><mi>s</mi><mi>s</mi><mi>o</mi><mi>c</mi><mi>i</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>W</mi><mi>i</mi><mi>t</mi><mi>h</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>e</mi><mi>d</mi><mi>O</mi><mi>n</mi><mi>B</mi><mi>e</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>f</mi><mi>O</mi><mi>f</mi><mo fence="false" stretchy="false">}</mo></math></span></span></span><script type="math/tex" id="MathJax-Element-669">r \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script>, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-670-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>p</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>a</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>a</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">,</mo><mo stretchy="false">…</mo><mo stretchy="false">,</mo><msub><mi>b</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-670">\begin{array}[t]{l}
 \forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
 \\
 \qquad p(id,a_1,\ldots,a_m) \wedge r(id,b_1,\ldots,b_n)
@@ -2889,7 +3048,7 @@
   from other objects (entities, activities or agents).
   </p>
   </div>
-<div class="constraint" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-639-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-639">\begin{array}[t]{l}
+<div class="constraint" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-671-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>i</mi><mi>d</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">,</mo><mi>a</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-671">\begin{array}[t]{l}
 \forall id.~
 \\
 \qquad typeOf(id,entity) \wedge typeOf(id,activity)
@@ -2901,7 +3060,7 @@
   <p>This follows from the assumption that entities and activities are disjoint.
   </p>
   </div>
-<div class="constraint" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-640-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>s</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-640">\begin{array}[t]{l}
+<div class="constraint" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-672-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable align="baseline 1" columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">∀</mi><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo>.</mo><mtext>&nbsp;</mtext></mtd></mtr><mtr><mtd><mspace width="2em"></mspace><mi>h</mi><mi>a</mi><mi>s</mi><mi>M</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>e</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mi>O</mi><mi>f</mi><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">,</mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>v</mi><mo stretchy="false">:</mo><mi>E</mi><mi>m</mi><mi>p</mi><mi>t</mi><mi>y</mi><mi>C</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mspace width="1em"></mspace><mo stretchy="false">⇒</mo><mi>F</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></math></span></span></span><script type="math/tex" id="MathJax-Element-672">\begin{array}[t]{l}
 \forall c,e.~
 \\
 \qquad hasMember(c,e) \wedge typeOf(c,prov:EmptyCollection)
@@ -2919,35 +3078,37 @@
 <!--OddPage--><h2><span class="secno">6. </span>Soundness</h2>
 
 <p>Above we have presented arguments for the soundness of the
-constraints and inferences with respect to the reference semantics.
-This implies the following:
-
-</p><div class="theorem" id="soundness-theorem" data-count="32" data-title="Theorem 32 (soundness-theorem)"><div class="ruleTitle"><a class="internalDFN" href="#soundness-theorem">Theorem 32 (soundness-theorem)</a></div>
+constraints and inferences with respect to the naive semantics.
+Here, we relate the notions of <dfn id="dfn-validity">validity</dfn> and <dfn id="dfn-normal-form">normal
+form</dfn> defined in PROV-CONSTRAINTS to the semantics.  
+Our main observation is:</p>
+
+<div class="theorem" id="soundness-theorem" data-count="33" data-title="Theorem 33 (soundness-theorem)"><div class="ruleTitle"><a class="internalDFN" href="#soundness-theorem">Theorem 33 (soundness-theorem)</a></div>
   <ol>
-  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-641-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-641">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-642-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-642">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-643-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-643">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-644-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-644">I</script> by applying one
-  of the PROV inferences, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-645-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-645">W \models I'</script>.</li>
-  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-646-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-646">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-647-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-647">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-648-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-648">I</script> has a normal
-  form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-649-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-649">I'</script> and   <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-650-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-650"> W \models I'</script>.</li>
-  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-651-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-651">I</script> is a normal form and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-652-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-652">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-653-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-653">I</script> satisfies all of the ordering,
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-673-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-673">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-674-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-674">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-675-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-675">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-676-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-676">I</script> by applying one
+  of the PROV inferences, then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-677-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-677">W \models I'</script>.</li>
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-678-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-678">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-679-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-679">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-680-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-680">I</script> has a normal
+  form <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-681-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-681">I'</script> and   <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-682-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-682"> W \models I'</script>.</li>
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-683-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-683">I</script> is a normal form and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-684-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-684">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-685-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-685">I</script> satisfies all of the ordering,
   typing and impossibility constraints.
-  </li><li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-654-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-654">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-655-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-655">I</script> is valid.</li>
+  </li><li>If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-686-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-686">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-687-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-687">I</script> is valid.</li>
 </ol>
   </div>
 <div class="proof">
   <p>For part 1, the arguments are as in the previous section.  </p>
   <p>For
   part 2, proceed by induction on a terminating sequence of inference
-  or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-656-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-656">I</script> is in normal form them we are
-  done. If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-657-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-657">I</script> is not in normal form then if an inference is  applicable, then use part 1; if a uniqueness constraint is
-  applicable, then from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-658-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-658">W \models I</script> the uniqueness constraint cannot
-  fail on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-659-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-659">I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-660-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-660">W \models I'</script>.</p>
+  or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-688-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-688">I</script> is in normal form them we are
+  done. If <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-689-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-689">I</script> is not in normal form then if an inference is  applicable, then use part 1; if a uniqueness constraint is
+  applicable, then from <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-690-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-690">W \models I</script> the uniqueness constraint cannot
+  fail on <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-691-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-691">I</script> and <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-692-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-692">W \models I'</script>.</p>
 <p>
   For part 3, the arguments are as
   in the previous section for each constraint. </p>
   <p>Finally, for part 4,
-  suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-661-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-661">W \models I</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-662-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-662">W \models I'</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-663-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-663">I'</script> is the normal
-  form of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-664-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-664">I</script> by part 2.  By part 3, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-665-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-665">I'</script> satisfies all of the
-  remaining constraints, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-666-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-666">I</script> is valid.</p>
+  suppose <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-693-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-693">W \models I</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-694-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo stretchy="false">⊨</mo><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-694">W \models I'</script> where <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-695-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-695">I'</script> is the normal
+  form of <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-696-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-696">I</script> by part 2.  By part 3, <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-697-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>I</mi><mo>′</mo></msup></math></span></span></span><script type="math/tex" id="MathJax-Element-697">I'</script> satisfies all of the
+  remaining constraints, so <span class="MathJax_Preview"></span><span class="MathJax_MathML" id="MathJax-Element-698-Frame" style="font-size: 100%; "><span class="MathJax_MathContainer" style="position: relative; display: inline-block; white-space: nowrap; "><span style="display: inline-block; "><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span></span><script type="math/tex" id="MathJax-Element-698">I</script> is valid.</p>
   </div>
 
 
@@ -3104,6 +3265,5 @@
 </dd><dt id="bib-PROV-O">[PROV-O]</dt><dd>Timothy Lebo; Satya Sahoo; Deborah McGuinness; eds. <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/"><cite>PROV-O: The PROV Ontology</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">http://www.w3.org/TR/2013/PR-prov-o-20130312/</a>
 </dd><dt id="bib-PROV-OVERVIEW">[PROV-OVERVIEW]</dt><dd>Paul Groth; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/"><cite>PROV-OVERVIEW: An Overview of the PROV Family of Documents</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/">http://www.w3.org/TR/2013/WD-prov-overview-20130312/</a>
 </dd><dt id="bib-PROV-PRIMER">[PROV-PRIMER]</dt><dd>Yolanda Gil; Simon Miles; eds. <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/"><cite>PROV Model Primer</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">http://www.w3.org/TR/2013/WD-prov-primer-20130312/</a>
-</dd><dt id="bib-PROV-SEM">[PROV-SEM]</dt><dd>James Cheney; ed. <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312"><cite>Semantics of the PROV Data Model</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312">http://www.w3.org/TR/2013/WD-prov-sem-20130312</a>.
 </dd><dt id="bib-PROV-XML">[PROV-XML]</dt><dd>Hook Hua; Curt Tilmes; Stephan Zednik; eds. <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/"><cite>PROV-XML: The PROV XML Schema</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">http://www.w3.org/TR/2013/WD-prov-xml-20130312/</a>
 </dd></dl></section></section></body></html>
\ No newline at end of file
--- a/semantics/prov-sem.html	Thu Feb 28 17:52:30 2013 +0000
+++ b/semantics/prov-sem.html	Fri Mar 01 15:49:14 2013 +0000
@@ -892,7 +892,7 @@
 };
       var respecConfig = {
           // specification status (e.g. WD, LCWD, NOTE, etc.). If in doubt use ED.
-          specStatus:           "ED",
+          specStatus:           "WD-NOTE",
           
           // the specification's short name, as in http://www.w3.org/TR/short-name/
           shortName:            "prov-sem",
@@ -904,7 +904,7 @@
 
 
           // if you wish the publication date to be other than today, set this
-         // publishDate:  "",
+         publishDate:  "2013-03-12",
 
           // if the specification's copyright date is a range of years, specify
           // the start date here:
@@ -976,11 +976,11 @@
 
 
 <p> This document presents a model-theoretic semantics for the PROV
-data model (called the <dfn>reference semantics</dfn>), viewing
+data model (called the <dfn>naive semantics</dfn>), viewing
 PROV-DM statements as atomic formulas in the sense of first-order
 logic, and viewing the constraints and inferences specified in
 PROV-CONSTRAINTS as a first-order theory. It is shown that the
-first-order theory is sound with respect to the reference semantics.
+first-order theory is sound with respect to the naive semantics.
 This information may be useful to researchers or users of PROV to
 understand the intended meaning and use of PROV for modeling
 information about the actual history, derivation or evolution of Web
@@ -988,7 +988,7 @@
 constraints or inferences for reasoning about PROV or integration of
 PROV with other Semantic Web vocabularies.  It is <b>not</b> proposed
 as a canonical or required semantics of PROV and does not place any
-constraints on use of PROV.</p>
+constraints on the use of PROV.</p>
 
 <p>The PROV Document Overview describes the overall state of PROV, and should be read before other PROV documents.</p>
 </section>
@@ -1003,12 +1003,18 @@
 <li> <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> (Proposed Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [[PROV-O]];</li>
 <li> <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> (Proposed Recommendation), the PROV data model for provenance [[PROV-DM]];</li>
 <li> <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> (Proposed Recommendation), a notation for provenance aimed at human consumption [[PROV-N]];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> (Proposed Recommendation), a set of constraints applying to the PROV data model  (this document);</li>
+<li> <a
+href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a>
+(Proposed Recommendation), a set of constraints applying to the PROV
+data model [[PROV-CONSTRAINTS]];</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> (To be published as Note),  an XML schema for the PROV data model [[PROV-XML]];</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">PROV-AQ</a> (To be published as Note), the mechanisms for accessing and querying provenance [[PROV-AQ]]; </li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">PROV-DICTIONARY</a> (To be published as Note) introduces a specific type of collection, consisting of key-entity pairs [[PROV-DICTIONARY]];</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> (To be published as Note) provides a mapping between PROV and Dublic Core Terms [[PROV-DC]];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> (To be published as Note), a declarative specification in terms of first-order logic of the PROV data model [[PROV-SEM]];</li>
+<li> <a
+href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a>
+(To be published as Note), a declarative specification in terms of
+first-order logic of the PROV data model (this document);</li>
 <li> <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> (To be published as Note) introduces a mechanism to link across bundles [[PROV-LINKS]].</li>
 </ul>
 
@@ -1028,7 +1034,7 @@
 [[PROV-CONSTRAINTS]] that
 specifies definitions, inferences, and constraints that can be used to
 reason about PROV documents, or determine their validity.  This document
-provides a reference formal semantics of PROV, providing a formal
+provides a naive formal semantics of PROV, providing a formal
 counterpart to the informal descriptions and motivations given
 elsewhere in PROV specifications.</p>
 
@@ -1079,19 +1085,33 @@
 building upon PROV.  It is intended as an exploration of a <b>reference</b>
 semantics for PROV, not a definitive specification of the  <b>only</b>
 semantics of PROV.  </p>
-
-<p> Nevertheless, the reference semantics does have appealing
+<div class="note">
+  <p>Clarify role of the semantics - too defensive?</p>
+  </div>
+
+<p> Although it is a work in progress, the naive semantics has some appealing
 properties.  Specifically, it provides a declarative counterpart to
 the operational definition of validity taken in PROV-CONSTRAINTS.  In
 the specification, validity is defined via a normalization process
 followed by constraint checking on the normal form.  This approach was adopted
 to keep the specification closer to implementations, although other
 implementations are possible and allowed.  In addition to providing a
-reference semantics, this document shows that the operational
+naive semantics, this document shows that the operational
 presentation of PROV validity checking is sound with respect to
 declarative presentation adopted here.  This could help justify
 alternative approaches to validity checking.</p>
 
+<p>This document mostly considers the semantics of PROV statements and
+  instances.  PROV documents can consist of multiple instances, and
+  the semantics does not (as yet) cover PROV documents, but the
+  semantics can be used on each instance in a document separately,
+  just as PROV-CONSTRAINTS specifies that each instance in a document
+  is to be validated separately.
+  So, in the rest of this document, we do not discuss PROV documents.
+  The semantics of other features of PROV, such as dictionaries
+  [[PROV-DICTIONARY]] and linking across bundles [[PROV-LINKS]], are
+  beyond the scope of this document.  </p>
+  
 <section> <h4>Structure of this document</h4> <p>
 
 </p>
@@ -1110,16 +1130,13 @@
   <li><a href="#theory">Section 5</a> presents the inferences and
   constraints from PROV-CONSTRAINTS as first-order formulas, and gives
   brief justifications for their soundness.</li>
-  <li><a href="#soundness">Section 6</a> relates the PROV notion of
-  validity to the logical notion of consistency.  A PROV instance is
-  valid if and only if its corresponding first-order theory is
-  satisfiable.</li>
+  <li><a href="#soundness">Section 6</a> summarizes the main result: soundness of
+the theory introduced in section 5 with respect to reference
+  semantics.  Completeness does not hold for the naive semantics</li>
 </ul>
 <div class="note">
-  Completeness direction above doesn't hold for current semantics,
-  because attributes assumed to be single-valued; for
-  example, $entity(id,[a=1,a=2])$ is valid but doesn't have a
-  reference model.
+<p>TODO: We would like to say something stronger here, such as a
+  completeness result, but this will take more work.</p>
   </div>
 
 </section>
@@ -1199,7 +1216,13 @@
 <h3> Identifiers </h3>
 
 <p>A lowercase symbol $x,y,...$ on its own denotes an identifier.
-Identifiers may or may not be URIs.  Identifiers are viewed as variables in logic (or blank nodes in RDF): just because we have two different identifiers $x$ and $y$ doesn't tell us that they denote different things, since we could discover that they are actually the same later.  We write $Identifiers$ for the set of identifiers of interest in a given situation (typically, the set of identifiers present in the PROV instance of interest).
+Identifiers may or may not be URIs.  Identifiers are viewed as
+variables from the point of view of logic: they denote objects, but
+just because we have two different identifiers $x$ and $y$ doesn't
+tell us that they denote different objects, since we could discover
+that they are actually the same later.  We write $Identifiers$ for the
+set of identifiers of interest in a given situation (typically, the
+set of identifiers present in the PROV instance of interest).
 </p>
 </section>
 
@@ -1208,6 +1231,10 @@
 
 <p>We assume a linearly ordered set $(Times,\leq)$ of time instants.  For convenience we assume the order is total or linear order, corresponding to a linear timeline; however, PROV does not assume that time is linear and events could be partially ordered and not necessarily reconciled to a single global clock.  
 </p>
+<div class="note">
+  Discuss implications of restricting attention to a linear order.
+  </div>
+
 <p>We also consider a set $Intervals$ of closed intervals of the form $\{t \mid t_1 \leq t \leq t_2\}$.
 </p>
 </section>
@@ -1226,7 +1253,12 @@
 
 <p>The following atomic formulas correspond to the statements of PROV-DM.  We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation $r(id,a_1,\ldots,a_n)$ instead of the semicolon notation $r(id;a_1,\ldots,a_n)$.
 </p>
-<p>Each parameter is either an identifier, a constant (e.g. a time or other literal value in an attribute list), or a null symbol "-".  Null symbols can only appear in the specified arguments in $wasAssociatedWith$ and $wasDerivedFrom$, as shown in the grammar below.
+<p>Each parameter is either an identifier, a constant (e.g. a time or
+  other literal value in an attribute list), or a null symbol "-".
+  Time parameters ($st,et$ in $activity$, and $t$ in generation,
+  usage, invalidation, start and end) are always constant time
+  literals.  Placeholder symbols $-$ can only appear in the specified arguments
+  $pl$ in $wasAssociatedWith$ and $a,g,u$ in $wasDerivedFrom$, as shown in the grammar below.
 </p>
 $$
 \begin{array}{rcl}
@@ -1241,8 +1273,8 @@
           &{::=}& wasGeneratedBy(id,e,a,t,attrs)\\
           & |&  used(id,e,a,t,attrs)\\
           & |&  wasInvalidatedBy(id,e,a,t,attrs)\\
-          & |&  wasStartedBy(id,a_2,e,a_1,attrs)\\
-          & |&  wasEndedBy(id,a_2,e,a_1,attrs)\\
+          & |&  wasStartedBy(id,a_2,e,a_1,t,attrs)\\
+          & |&  wasEndedBy(id,a_2,e,a_1,t,attrs)\\
           & |&  wasAssociatedWith(id,ag,act,pl,attrs)\\
           & |&  wasAssociatedWith(id,ag,act,-,attrs)\\
           & |&  wasAttributedTo(id,e,ag,attrs)\\
@@ -1268,7 +1300,18 @@
 &|& prov:EmptyCollection
 \end{array}
 $$
-
+<div class="note">
+  Remove prefixes from prov:Collection and prov:EmptyCollection?
+  </div>
+
+  <div class="note">
+    Restate that we are not modeling documents/bundles, however eachi
+    instance can be modeled separately.
+    </div>
+
+    <div class="note">
+      similar question: can we try to handle mentionOf?
+      </div>
 </section>
 
 <section>
@@ -1315,13 +1358,13 @@
 <h3> Things </h3> 
 
 <div class="note">TODO: Containment of things / collections? (for hadMember).</div>
-<p><em>Things</em> are things in the world.  Each thing has a lifetime during which it exists and attributes whose values can change over time.
+<p><em>Things</em>  is a set of things in the situation being modeled.  Each thing has a lifetime during which it exists and attributes whose values can change over time.
 </p>
 <p>To model this, a structure $W$ includes:
 </p>
 <div class="component" id="things"><ol>
   <li> a set $Things$ of things</li>
-  <li> a function $lifetime : Things \to Intervals$ from objects to time intervals</li>
+  <li> a function $lifetime : Things \to Intervals$ from things to time intervals</li>
   <li>a function $value : Things \times Attributes \times Times \to P(Values)$
 </li>
 </ol>
@@ -1333,14 +1376,18 @@
 
 <p>Note that this description does not say what the structure of a
 $Thing$ is, only how it may be described in terms of its time interval
-and attribute values.  An object could just be a record of fixed
+and attribute values.  A thing could be a record of fixed
 attribute values; it could be a bear; it could be the Royal Society;
 it could be a transcendental number like $\pi$.  All that matters from
 our point of view is that we know how to map the $Thing$ to its time interval and attribute mapping.
 </p>
 
 
-<p>It is possible for two Things to be indistinguishable by their attribute values and lifetime, but have different identity.
+<p>The identity of a Thing is not observable through its attributes or
+lifetime, so it is possible for two different Things to be indistinguishable by their
+attribute values and lifetime.  That is, if the set of $Things = \{T_0,T_1\}$ and the attributes are
+specified as $value(T_0,a,t) = value(T_1,a,t)$ for each $t\in
+Times$ and $a \in Attributes$, this does not imply that $T_0 = T_1$.
 </p>
 
 
@@ -1349,8 +1396,15 @@
 <section>
 <h3> Objects </h3>
 
+<div class="note">
+  TODO: Add text explaining the relationship between Things and
+  Objects.
+</div>
+
 <p>
-An <em>Object</em> is described by a time interval and attributes with unchanging values.  Objects encompass entities, interactions, and activities.
+An <em>Object</em> is described by a time interval and attributes with
+fixed values.  Objects encompass entities, activities, agents, and
+interactions (i.e., usage, generation, and other events or influence relations).
 To model this, a structure includes:
 </p>
 
@@ -1366,13 +1420,22 @@
 </p>
 
 <p>As with <em>Things</em>, the range of $value$ is sets of values,
-making $value$ effectively a multivalued function.  It is also possible to have two different objects that are indistinguishable by their attributes and time intervals.  Objects are not things, and the sets of $Objects$ and $Things$ are disjoint; however, certain objects, namely entities, are linked to things.
-
+making $value$ effectively a multivalued function.  It is also
+possible to have two different objects that are indistinguishable by
+their attributes and time intervals.  Objects are not things, and the
+sets of $Objects$ and $Things$ are disjoint; however, certain objects,
+namely entities, are associated with things.
 </p>
+
+<div class="note">
+  Disjointness between object and thing is not necessary but is
+  assumed in order to avoid confusion between the different categories
+  (time-varying vs fixed); nothing changes if we allow them to overlap.
+  </div>
 <section>
 <h4> Entities </h4>
 
-An <em>entity</em> is a kind of object that describes a time-slice of a thing, during which some of the thing's attributes are fixed. We assume:
+<p>An <em>entity</em> is a kind of object that describes a time-slice of a thing, during which some of the thing's attributes are fixed. We assume:</p>
 
 <div class="component" id="entities">
   <ol><li> a set $Entities \subseteq Objects$ of entities, disjoint from $Activities$ and $Events$ below.
@@ -1385,20 +1448,31 @@
   undefined or multiple attribute values, their meaning is slightly
   different: for a thing, $value(x,a,t) = \emptyset$ means that the
   attribute $a$ has no value at time $t$, whereas for an entity,
-  $value(x,a) = \emptyset$ only means that the entity does not record
-  a fixed value for $a$ forthe associated thing.  This does not imply
+  $value(x,a) = \emptyset$ only means that the thing associated to
+  entity $x$ does not have a
+  fixed value for $a$ during the lifetime of $x$.  This does not imply
   that $value(thingOf(e),a,t) = \emptyset$ when $t \in lifetime(e)$.
-</p>
-  <p>Furthermore, all of the attribute values of the entity must be
-  present in the associated thing throughout the lifetime of the entity.
-For example, suppose $value(thingOf(e),a,t)$ is $\{1\}$ at some
-time in $lifetime(e)$ and $value(thingOf(e),a,t') = \{2\}$ at some
-  other time $t'$.  Then $value(e,a)$ must be $\emptyset$ because
+  </p>
+
+  <p>Furthermore, all of the attribute values of the entity must
+  be present in the associated thing throughout the lifetime of the
+  entity.  For example, suppose $value(thingOf(e),a,t)$ is $\{1\}$ at
+  some time in $lifetime(e)$ and $value(thingOf(e),a,t') = \{2\}$ at
+  some other time $t'$.  Then $value(e,a)$ must be $\emptyset$ because
   there is no other set of values that is simultaneously contained in
-  both $\{1\}$ and $\{2\}$.
-</p>
+  both $\{1\}$ and $\{2\}$.  </p> </div>
+
+<div class="note">
+  Can we give further intuiton for the $value(obj,a) \subseteq
+  value(thingOf(obj),a,t)$ and what it tells us about objects
+  vs. things?
   </div>
-
+  
+<div class="note">
+TODO:   Is there a reason why only Entities are assciated with Things,
+  rather than allowing all Objects to be associated with Things?
+  </div>
+  
 <section>  
 <h5> Plans </h5>
 <p>We identify a specific subset of the entities called
@@ -1411,7 +1485,7 @@
   </section>
 
     <section>
-<h4> Actvities </h4>
+<h4> Activities </h4>
 
 
 <p>An <em>activity</em> is an object that encompasses a set of events.  We introduce
@@ -1427,14 +1501,19 @@
 <h4> Agents </h4>
 
 <p>An agent is an object that can act, by controlling, starting,
-  ending, or participating in activities.  Agents can act on behalf of
-  other agents. An agent can be an entity, an activity, or neither; an
+  ending, or participating in activities.  An agent is something that
+  bears some form of responsibility for an activity taking place, for
+  the existence of an entity, or for another agent's activity.  Agents can act on behalf of
+  other agents. An agent may be a particular type of entity or activity; an
   agent cannot be both entity and activity because the sets of
   entities and activities are disjoint.  We introduce:
 </p>
 <div class="component" id="agents">
   <p>A set $Agents \subseteq Objects$ of agents.</p>
   </div>
+  <div class="remark">
+    <p>There is no requirement that every agent is either an activity
+  or an entity. </p>
 </section>
 
 
@@ -1445,14 +1524,16 @@
   <em>Events</em> connecting entities and activities,
   <em>Associations</em> between agents and activities,
   <em>Communications</em> between pairs of activities,
-  <em>Delegations</em> between pairs of agents, and <em>Derivations</em> that describe chains of generation and usage steps.  (The first two sets may overlap.)  Interactions are disjoint from entities, activities and agents.
+  <em>Delegations</em> between pairs of agents, and
+  <em>Derivations</em> that describe chains of generation and usage
+  steps.  These kinds of interactions are discussed further below.  Interactions are disjoint from entities, activities and agents.
 </p>
 <div class="component" id="interactions">
   <ol><li> A set $Interactions = Events \cup Associations \cup
   Communications \cup Delegations \cup Derivations \subseteq Objects$
 </li>
 <li> A function $type: Interactions \to
-  \{start,end,usage,generation,invalidation,derivation,version,quotation,primarySource,attribution,delegation\}$.
+  \{start,end,usage,generation,invalidation,derivation,revision,quotation,primarySource,attribution,delegation\}$.
 </li>
 <li> The sets $Events$, $Associations$, $Communications$, $Delegations$
   and $Derivations$ are all disjoint.
@@ -1461,6 +1542,11 @@
 </li></ol>
 </div>
 
+<div class="note">
+  Explain why the different subsets of interactions are disjoint.
+  This is necessary in order for constraint 53 to hold.
+  </div>
+
 <section>
 <h5> Events </h5>
 
@@ -1471,8 +1557,8 @@
 <div class="component" id="events">
 <ol><li> A set $Events \subseteq Interactions$ of events, such that
   $type(evt) \in \{start,end,generation,usage,invalidation\}$ if and
-  only of $evt \in Events$.
-</li><li> A function $time : Events \to Times$ giving the time of each event; i.e. $lifetime(evt) = \{time(t)\}$.
+  only if $evt \in Events$.
+</li><li> A function $time : Events \to Times$ giving the time of each event; i.e. $lifetime(evt) = \{time(evt)\}$.
 </li><li> The derived ordering on events given by $evt_1 \leq evt_2 \iff time(evt_1) \leq time(evt_2)$
 </li></ol>
 </div>
@@ -1510,11 +1596,14 @@
 </p>
 <div class="component" id="derivations">
 <p>  A set $Derivations \subseteq Interactions$, such that
-  $type(deriv) \in \{derivation, version, primarySource,quotation\}$
+  $type(deriv) \in \{derivation, revision, primarySource,quotation\}$
   if and only if $deriv \in Derivations$.
 </p></div>
 <p>See below for the associated derivation path and DerivedFrom relation.
 </p>
+<div class="note">TODO: Clarify that existence of a chained generation
+  and use step does not necessarily imply derivation</div>
+  
 </section>
 </section>
 </section>
@@ -1525,11 +1614,11 @@
 <h4> Simple relations </h4>
 <p>The entities, interactions, and activities in a structure are related in the following ways:
 </p>
-<ol><li> A relation $Used \subseteq Events \times Entities$ saying when an event used an entity.  An event can use at most one entity, and if $(evt,e)\in Used$ then $time(evt) \in lifetime(e)$ and $type(g) = use$ must hold.
-</li><li> A relation $Generated \subseteq Events \times Entities$ saying when an event generated an entity.  An event can generate at most one entity, and if $(evt,e)\in Generated$ then $min(lifetime(e)) = time(evt)$ and $type(g) = generation$ must hold.
-</li><li> A relation $Invalidated \subseteq Events \times Entities$ saying when an event invalidated an entity.  An event can invalidate at most one entity, and if $(evt,e)\in Invalidated$ then $min(lifetime(e)) = time(evt)$ and $type(g) = invalidation$ must hold.
+<ol><li> A relation $Used \subseteq Events \times Entities$ saying when an event used an entity.  An event can use at most one entity, and if $(evt,e)\in Used$ then $time(evt) \in lifetime(e)$ and $type(evt) = usage$ must hold.
+</li><li> A relation $Generated \subseteq Events \times Entities$ saying when an event generated an entity.  An event can generate at most one entity, and if $(evt,e)\in Generated$ then $min(lifetime(e)) = time(evt)$ and $type(evt) = generation$ must hold.
+</li><li> A relation $Invalidated \subseteq Events \times Entities$ saying when an event invalidated an entity.  An event can invalidate at most one entity, and if $(evt,e)\in Invalidated$ then $max(lifetime(e)) = time(evt)$ and $type(evt) = invalidation$ must hold.
 </li><li> A relation $EventActivity \subseteq Events \times Activities$ associating activities with events, such that $(act,evt) \in EventActivity$ implies $time(evt) \in lifetime(act)$.
-</li><li> A relation $AssociatedWith \subseteq Association \times Agents \times Activities \times Plans_\bot$ indicating when an agent is associated with an activity, and giving the identity of the association relationship, and an optional plan. 
+</li><li> A relation $AssociatedWith \subseteq Associations \times Agents \times Activities \times Plans_\bot$ indicating when an agent is associated with an activity, and giving the identity of the association relationship, and an optional plan. 
 </li><li> A relation $ActsFor \subseteq Delegations \times Agents \times Agents \times Activities$ indicating when one agent acts on behalf of another with respect to a given activity.  
 </li></ol>
 
@@ -1541,6 +1630,11 @@
   TODO: Specialization relation
   </div>
 
+<div class="note">
+  EventActivity allows an event not to be associated with any
+  activity.  Is this OK?
+  </div>
+  
   <div class="note">
     TODO: Explicit axioms concerning the relations
   </div>
@@ -1563,16 +1657,33 @@
 <p>with the constraints that for each derivation path:
 </p>
 <ul>
-<li>for each substring $ent\cdot g \cdot act$ we have $(g,ent) \in Generated$  and $(g,act) \in EventActivities$, and
+<li>for each substring $ent\cdot g \cdot act$ we have $(g,ent) \in Generated$  and $(g,act) \in EventActivity$, and
 </li>
-<li>for each substring $act \cdot u \cdot ent$ we have $(u,ent) \in Used$ and $(u,act) \in EventActivities$.
+<li>for each substring $act \cdot u \cdot ent$ we have $(u,ent) \in Used$ and $(u,act) \in EventActivity$.
 </li>
 </ul>
-<p>We also consider a function $derivedFrom : Derivations \to
-DerivationPaths$  linking each derivation to its path.</p>
-
-
-<div class="remark">The reason why we need paths and not just individual derivation steps is that imprecise wasDerivedFrom formulas can represent multiple derivation steps.</div>
+<p>Each derivation $d \in Derivations$ has an associated derivation path.  We link each derivation to an associated derivation path using the
+function $derivationPath : Derivations \to
+DerivationPaths$.  </p>
+
+<div class="remark">
+  <p>
+  The $derivationPath$ function links each $ d \in Derivations$ to a
+  derivation path.  A derivation has exactly one associated derivation
+  path.  However, if the PROV-N statement <span
+  class="name">wasDerivedFrom(e_2,e_1,-,-,-)</span> is asserted in an
+  instance, there may be multiple derivation paths linking $e_2$ to
+  $e_1$, each corresponding to a different, identified by different
+  derivations $d \in Derivations$.
+  </p>
+  </div>
+
+<div class="note">
+  We can make the characterization of DerivationPaths more
+  precise/concise by introducing sets of Usage and Generation events.
+</div>
+
+<div class="remark">The reason why we need paths and not just individual derivation steps is that $wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)$ formulas can represent multiple derivation steps.</div>
 </section>
 </section>
 
@@ -1586,6 +1697,10 @@
 decrease notational clutter, when we consider a fixed structure then the names of the sets, relations and functions above refer to the components of that model.
 </p>
 
+<div class="note">
+  TODO: Highlight the distinctive vs obvious/routine features.
+  </div>
+
 </section>
 <section>
 <h3> Interpretations </h3>
@@ -1691,7 +1806,8 @@
 
 </div>
 <div class="remark">
-<p>For example, the following formulas all hold if $x$ denotes an entity $e$ such that $value(e,a) = \{4,5\}, value(e,b) = \{6\}$ hold:
+<p>Not all of the attributes of an entity object are
+  required to be present in an entity formula about that object.  For example, the following formulas all hold if $x$ denotes an entity $e$ such that $value(e,a) = \{4,5\}, value(e,b) = \{6\}$ hold:
 </p><pre>
  entity(x,[])
  entity(x,[a=5])
@@ -1722,9 +1838,9 @@
 <ol>
 <li>[WF] The identifier $id$ maps to an activity $act = \rho(id) \in Activities$
 </li>
-<li>If $st$ is specified then it is equal to the start time of the activity, that is: $min(lifetime(id)) = st$
+<li>$st$ is the activity's start time, that is: $min(lifetime(id)) = st$
 </li>
-<li>If $et$ is specified then it is equal to the end time of the activity, that is: $max(lifetime(id)) = et$
+<li>$et$ is the activity's end time, that is: $max(lifetime(id)) = et$
 </li>
 <li>The attributes match: $match(W,act,attrs)$.
 </li>
@@ -1772,7 +1888,7 @@
 </li>
 <li>[WF] The identifier $a$ denotes an activity $act = \rho(a) \in Activities$.
 </li>
-<li>The event $evt$ is involved in $act$, that is, $(evt,act) \in EventActivities$.
+<li>The event $evt$ is involved in $act$, that is, $(evt,act) \in EventActivity$.
 </li>
 <li>The type of $evt$ is $generation$, i.e. $type(evt) = generation$.
 </li>
@@ -1801,7 +1917,7 @@
 </li>
 <li>[WF] The identifier $e$ denotes an entity $ent = \rho(e) \in Entities$.
 </li>
-<li>The event $evt$ is part of $act$, i.e. $(evt,act) \in EventActivities$.
+<li>The event $evt$ is part of $act$, i.e. $(evt,act) \in EventActivity$.
 </li>
 <li>The type of $evt$ is $use$, i.e., $type(evt) = use$.
 </li>
@@ -1827,7 +1943,7 @@
 </li>
 <li>[WF] The identifier $a$ denotes an activity $act = \rho(a) \in Activities$.
 </li>
-<li>The event $evt$ is involved in $act$, that is, $(evt,act) \in EventActivities$.
+<li>The event $evt$ is involved in $act$, that is, $(evt,act) \in EventActivity$.
 </li>
 <li>The type of $evt$ is $invalidation$, i.e. $type(evt) = invalidation$.
 </li>
@@ -1854,20 +1970,34 @@
 </li>
 <li>[WF] $ag$ denotes an agent $agent = \rho(ag) \in Agents$.
 </li>
-<li>[WF] $pl$ is either the placeholder $-$ or denotes a plan $plan=\rho(pl) \in Plans$.
+<li>[WF] $pl$ denotes a plan $plan=\rho(pl) \in Plans$.
 </li>
 <li>The association associates the agent with the activity and plan, i.e. $(assoc,agent,act,plan) \in AssociatedWith$.
 </li>
 <li>The attributes match: $match(W,assoc,attrs)$.
 </li></ol></div>
+
+<div class="formalism"><p>
+  $W,\rho \models wasAssociatedWith(id,a,ag,-,attrs)$ holds if and only if:</p>
+<ol>
+<li>[WF] $assoc$ denotes an association $assoc = \rho(id) \in Associations$.
+</li>
+<li>[WF] $a$ denotes an activity $act = \rho(a) \in Activities$.
+</li>
+<li>[WF] $ag$ denotes an agent $agent = \rho(ag) \in Agents$.
+</li>
+<li>The association associates the agent with the activity and plan, i.e. $(assoc,agent,act,\bot) \in AssociatedWith$.
+</li>
+<li>The attributes match: $match(W,assoc,attrs)$.
+</li></ol></div>
 </section>
 <section>
 <h5> Start Formulas </h5>
 
-<p>A start formula $wasStartedBy(id,a_2,e,a_1,attrs)$ is interpreted as follows:</p>
+<p>A start formula $wasStartedBy(id,a_2,e,a_1,t,attrs)$ is interpreted as follows:</p>
 
 <div class="formalism">
-  <p>$W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)$ holds if and only if:</p>
+  <p>$W,\rho \models wasStartedBy(id,a_2,e,a_1,t,attrs)$ holds if and only if:</p>
 <ol>
 <li>[WF] $id$ denotes an event $evt = \rho(id) \in Events$.
 </li>
@@ -1880,7 +2010,7 @@
 <li>The event $evt$ has type $start$, i.e. $type(evt) = start$.
 </li>
 <li>The event happened at the start of $act_2$, that is, $(evt,act_2)
-  \in EventsActivities$, and $min(lifetime(act_2)) = time(evt)$.
+  \in EventsActivities$, and $t = min(lifetime(act_2)) = time(evt)$.
 </li>
 <li>TODO: The entity $e$ was generated by $act_1$ and started $act_2$.
 <li>The event happened during $act_1$, that is, $(evt,act_1)
@@ -1892,11 +2022,11 @@
 <section>
 <h5> End </h5>
 
-<p>An activity end formula $wasEndedBy(id,a_2,e,a_1,attrs)$ is interpreted as follows:</p>
+<p>An activity end formula $wasEndedBy(id,a_2,e,a_1,t,attrs)$ is interpreted as follows:</p>
 
 <div class="formalism">
 <p>
-  $W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)$ holds if and only
+  $W,\rho \models wasEndedBy(id,a_2,e,a_1,t,attrs)$ holds if and only
   if:</p>
   
 <ol>
@@ -1906,10 +2036,10 @@
 <li>[WF] $a_1$ denotes an activity $act_1 = \rho(a_1)\in Activities$.</li>
 <li>The event $evt$ has type $end$, i.e. $type(evt) = end$.</li>
 <li>The event happened at the end of $act_2$, that is, $(evt,act_2)
-  \in EventsActivities$, and $max(lifetime(act_2)) = time(evt)$.</li>
+  \in EventsActivities$, and $t = max(lifetime(act_2)) = time(evt)$.</li>
   <li>TODO: The entity $e$ was generated by $act_1$ and ended $act_2$.</li>
 
-<li>The event happened during $act_1$, that is, $(evt,act_1) \in EventActivities.</li>
+<li>The event happened during $act_1$, that is, $(evt,act_1) \in EventActivity.</li>
 <li>The attributes match: $match(W,evt,attrs)$.</li>
 </ol>
 </div>
@@ -1940,6 +2070,11 @@
 </div>
 </section>
 
+<div class="note">
+  TODO: Ensure that the semantics requires the agent's lifetime to
+  start before that of the entity.
+</div>
+
 <section>
 <h4>Communication</h4>
 <div class="note">TODO: Communication</div>
@@ -1974,6 +2109,16 @@
 
 <h5> Derivation </h5>
 
+<p>
+Derivation formulas can be of one of two forms:</p>
+<ul><li>$wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)$, which specifies an
+  activity, generation and usage event.  For convenience we call
+  a <dfn>precise derivation</dfn>.</li>
+  <li> and $wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)$, which does not
+  specify an activity, generation and usage event.  For convenience we
+  call this an <dfn>imprecise derivation</dfn>.</li>
+  </ul>
+
 <section>
 <h6> Precise </h6>
 
@@ -1992,7 +2137,7 @@
 </li>
 <li>[WF] $u$ denotes a use event $\rho(u) \in Events$ and $type(\rho(u)) = use$.
 </li>
-<li>The derivation denotes a one-step derivation $derivedFrom(deriv) =
+<li>The derivation denotes a one-step derivation $derivationPath(deriv) =
 ent_2 \cdot gen \cdot act \cdot use \cdot ent_1$.
 </li>
 <li>The attribute values match: $match(W,deriv,attrs)$.</li>
@@ -2012,7 +2157,7 @@
 </li>
 <li>[WF] $e_1,e_2$ denote entities $ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities$ 
 </li>
-<li>$derivedFrom(deriv)= ent_2 \cdot  w \cdot ent_1$ for some $w$
+<li>$derivationPath(deriv)= ent_2 \cdot  w \cdot ent_1$ for some $w$
 </li>
 <li>The attribute values match: $match(W,deriv,attrs)$.
 </li></ol></div>
@@ -2047,16 +2192,16 @@
 </li>
 <li>The two Entities refer to the same Thing, that is, $thingOf(ent_1) = thingOf(ent_2)$.
 </li>
-<li>The lifetime of $obj_1$ is contained in that of $ent_2$, i.e. $lifetime(ent_1) \subseteq lifetime(ent_2)$.
+<li>The lifetime of $ent_1$ is contained in that of $ent_2$, i.e. $lifetime(ent_1) \subseteq lifetime(ent_2)$.
 </li>
-<li>For each attribute $attr$ we have $value(obj_1,attr) \supseteq value(obj_2,attr)$.
+<li>For each attribute $attr$ we have $value(ent_1,attr) \supseteq value(ent_2,attr)$.
 </li></ol></div>
 
-<p>The second criterion says that the two Entities present aspects of
-the same Thing. Note that the third criterion allows $obj_1$ and
-$obj_2$ to have the same lifetime (or that of $obj_2$ can be larger).
-The last criterion allows $obj_1$ to have more defined attributes than
-$obj_2$, but they must include the attributes defined by $obj_2$.
+<p>The second criterion says that the two Entities present (possibly different) aspects of
+the same Thing. Note that the third criterion allows $ent_1$ and
+$ent_2$ to have the same lifetime (or that of $ent_2$ can be larger).
+The last criterion allows $ent_1$ to have more defined attributes than
+$ent_2$, but they must include the attributes defined by $ent_2$.
 </p>
 
 </section>
@@ -2126,7 +2271,7 @@
   <h4>Precedes and Strictly Precedes</h4>
   <p>The precedes relation $x \preceq y$ holds between two events, one taking
   place before (or simultaneously with) another.  Since the
-  reference semantics assumes that times are linearly ordered and
+naive semantics assumes that times are linearly ordered and
   event times are 
   mapped to a single time line, this amounts to
   comparing the event times.  The semantics of strictly precedes ($x
@@ -2139,6 +2284,23 @@
        $\rho(x),\rho(y) \in Events$ and $time(\rho(x)) < time(\rho(y))$.</li>
     </ol>
   </div>
+
+  <div class="remark">
+    <p> Because we use a linearly ordered time to define event
+    precedence, there are valid PROV instances that are not satisfied
+    in any naive model.  For example:</p>
+    <pre>
+entity(e)
+activity(a1)
+activity(a2)
+wasGeneratedBy(gen1; e, a1, 2011-11-16T16:05:00)
+wasGeneratedBy(gen2; e, a2, 2012-11-16T16:05:00) //different date
+</pre>
+    <p>This instance is valid, and must satisfy precedence constraints
+    $gen_1 \preceq gen_2$ and $gen_2 \preceq gen_1$, but $time(gen_1)=
+    </p>
+    
+  </div>
   </section>
   
   <section>
@@ -2189,7 +2351,7 @@
     In this section we restate all of the inferences and constraints
     of PROV-CONSTRAINTS in terms of first-order logic.  For each, we
     give a proof sketch showing why the inference or constraint is
-    sound for reasoning about the reference semantics.  We exclude the
+    sound for reasoning about the naive semantics.  We exclude the
     definitional rules in PROV-CONSTRAINTS because they are only
     needed for expanding the abbreviated forms of PROV-N statements to
     the logical formulas used here.</p>
@@ -2356,7 +2518,7 @@
 alternateOf(e,e)
 \end{array}$</div>
 <div class="proof">
-  <p> Suppose $ent = rho(e)$.  Clearly $e \in Entities$ and
+  <p> Suppose $ent = \rho(e)$.  Clearly $e \in Entities$ and
   $thingOf(e) = thingOf(e)$, so $W,\rho \models alternateOf(e,e)$.</p>
   </div>
 <div class="inference" number="17" id="alternate-transitive">$\begin{array}[t]{l}
@@ -2368,11 +2530,11 @@
 alternateOf(e_1,e_3)
 \end{array}$</div>
 <div class="proof">
-  <p> Suppose $ent_1 = rho(e_1)$ and $ent_2 = \rho(e_2)$ and $ent_3 = \rho(e_3)$.  Then  by
+  <p> Suppose $ent_1 = \rho(e_1)$ and $ent_2 = \rho(e_2)$ and $ent_3 = \rho(e_3)$.  Then  by
   assumption $ent_1$, $ent_2$, and $ent_3$ are in $Entities$ and
   $thingOf(e_1) = thingOf(e_2)$ and $thingOf(e_2) = thingOf(e_3)$, so
   $thingOf(e_1) = thingOf(e_3)$, as required to conclude $W,\rho
-  \models alternateOf(e_2,e_1)$.</p>
+  \models alternateOf(e_1,e_3)$.</p>
   </div>
 <div class="inference" number="18" id="alternate-symmetric">$\begin{array}[t]{l}
 \forall e_1,e_2.~
@@ -2383,7 +2545,7 @@
 alternateOf(e_2,e_1)
 \end{array}$</div>
 <div class="proof">
-  <p> Suppose $ent_1 = rho(e_1)$ and $ent_2 = \rho(e_2)$.  Then  by
+  <p> Suppose $ent_1 = \rho(e_1)$ and $ent_2 = \rho(e_2)$.  Then  by
   assumption both $ent_1$ and $ent_2$ are in $Entities$ and
   $thingOf(e_1) = thingOf(e_2)$, as required to conclude $W,\rho
   \models alternateOf(e_2,e_1)$.</p>
@@ -3015,8 +3177,10 @@
 <h2>Soundness</h2>
 
 <p>Above we have presented arguments for the soundness of the
-constraints and inferences with respect to the reference semantics.
-This implies the following:
+constraints and inferences with respect to the naive semantics.
+Here, we relate the notions of <dfn>validity</dfn> and <dfn>normal
+form</dfn> defined in PROV-CONSTRAINTS to the semantics.  
+Our main observation is:</p>
 
 <div class="theorem" id="soundness-theorem">
   <ol>
prov

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