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+ <body style="display: inherit;"><div style="visibility: hidden; overflow: hidden; position: absolute; top: 0px; height: 1px; width: auto; padding: 0px; border: 0px; margin: 0px; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal;"><div id="MathJax_Hidden"></div></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></p><h1 class="title" id="title">Semantics of the Provenance Data Model</h1><h2 id="w3c-editor-s-draft-17-december-2012"><acronym title="World Wide Web Consortium">W3C</acronym> Editor's Draft 17 December 2012</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><dt>Latest published version:</dt><dd><a href="http://www.w3.org/TR/prov-sem/">http://www.w3.org/TR/prov-sem/</a></dd><dt>Latest editor's draft:</dt><dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd><dt>Previous version:</dt><dd>none</dd><dt>Editor:</dt><dd><a href="http://homepages.inf.ed.ac.uk/jcheney">James Cheney</a>, University of Edinburgh</dd>
+</dl><p class="copyright"><a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> © 2012-2012 <a href="http://www.w3.org/"><acronym title="World Wide Web Consortium">W3C</acronym></a><sup>®</sup> (<a href="http://www.csail.mit.edu/"><acronym title="Massachusetts Institute of Technology">MIT</acronym></a>, <a href="http://www.ercim.eu/"><acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym></a>, <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. <acronym title="World Wide Web Consortium">W3C</acronym> <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> rules apply.</p><hr></div><div id="MathJax_Message" style="display: none;">Loading [MathJax]/jax/output/HTML-CSS/fonts/STIX/fontdata.js</div>
+
+ <div id="abstract" class="introductory section"><h2>Abstract</h2>
+<p>
+Provenance is information about entities, activities, and people
+involved in producing a piece of data or thing, which can be used to
+form assessments about its quality, reliability or
+trustworthiness. PROV-DM is the conceptual data model that forms a
+basis for the <acronym title="World Wide Web Consortium">W3C</acronym> provenance (PROV) family of specifications.
+</p>
+
+
+<p> This document ... TODO </p>
+<p>The PROV Document Overview describes the overall state of PROV, and should be read before other PROV documents.</p>
+</div><div id="sotd" class="introductory section"><h2>Status of This Document</h2><p><em>This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current <acronym title="World Wide Web Consortium">W3C</acronym> publications and the latest revision of this technical report can be found in the <a href="http://www.w3.org/TR/"><acronym title="World Wide Web Consortium">W3C</acronym> technical reports index</a> at http://www.w3.org/TR/.</em></p>
+<h4 id="prov-family-of-documents">PROV Family of Documents</h4>
+This document is part of the PROV family of documents, a set of documents defining various aspects that are necessary to achieve the vision of inter-operable
+interchange of provenance information in heterogeneous environments such as the Web. These documents are:
+<ul>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/">PROV-OVERVIEW</a> (Note), an overview of the PROV family of documents [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-OVERVIEW">PROV-OVERVIEW</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/">PROV-PRIMER</a> (Note), a primer for the PROV data model [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-PRIMER">PROV-PRIMER</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/">PROV-O</a> (Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-O">PROV-O</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/">PROV-DM</a> (Recommendation), the PROV data model for provenance [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/">PROV-N</a> (Recommendation), a notation for provenance aimed at human consumption [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-N">PROV-N</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2012/CR-prov-constraints-20121211/">PROV-CONSTRAINTS</a>
+(Recommendation), a set of constraints applying to the PROV data model;</li>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/">PROV-AQ</a> (Note), the mechanisms for accessing and querying provenance [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-AQ">PROV-AQ</a></cite>]; </li>
+<li> <a href="http://www.w3.org/TR/2012/WD-prov-xml-20121211/">PROV-XML</a> (Note), an XML schema for the PROV data model [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-XML">PROV-XML</a></cite>].</li>
+
+</ul>
+<h4 id="how-to-read-the-prov-family-of-documents">How to read the PROV Family of Documents</h4>
+<ul>
+<li>The primer is the entry point to PROV offering an introduction to the provenance model.</li>
+<li>The Linked Data and Semantic Web community should focus on PROV-O defining PROV classes and properties specified in an OWL2 ontology. For further details, PROV-DM and PROV-CONSTRAINTS specify the constraints applicable to the data model, and its interpretation. </li>
+<li>Developers seeking to retrieve or publish provenance should focus on PROV-AQ.</li>
+<li>Readers seeking to implement other PROV serializations
+should focus on PROV-DM and PROV-CONSTRAINTS. PROV-O and PROV-N offer examples of mapping to RDF and text, respectively.</li>
+</ul>
+
+<p>This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as an Editor's Draft. If you wish to make comments regarding this document, please send them to <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a> (<a href="mailto:public-prov-comments-request@w3.org?subject=subscribe">subscribe</a>, <a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archives</a>). All feedback is welcome.</p><p>Publication as an Editor's Draft does not imply endorsement by the <acronym title="World Wide Web Consortium">W3C</acronym> Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than work in progress.</p><p>This document was produced by a group operating under the <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February 2004 <acronym title="World Wide Web Consortium">W3C</acronym> Patent Policy</a>. <acronym title="World Wide Web Consortium">W3C</acronym> maintains a <a href="http://www.w3.org/2004/01/pp-impl/46974/status" rel="disclosure">public list of any patent disclosures</a> made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential Claim(s)</a> must disclose the information in accordance with <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section 6 of the <acronym title="World Wide Web Consortium">W3C</acronym> Patent Policy</a>.</p></div><div id="toc" class="section"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1. </span>Introduction<br>
+</a><ul class="toc"><li class="tocline"><a href="#conventions" class="tocxref"><span class="secno">1.1 </span>Conventions</a></li><li class="tocline"><a href="#purpose" class="tocxref"><span class="secno">1.2 </span>Purpose of this document</a></li><li class="tocline"><a href="#structure-of-this-document" class="tocxref"><span class="secno">1.3 </span>Structure of this document</a></li><li class="tocline"><a href="#audience" class="tocxref"><span class="secno">1.4 </span> Audience </a></li></ul></li><li class="tocline"><a href="#test" class="tocxref"><span class="secno">2. </span>MathJax test</a></li><li class="tocline"><a href="#inferences" class="tocxref"><span class="secno">3. </span>Inferences</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="#normative-references" class="tocxref"><span class="secno">B.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">B.2 </span>Informative references</a></li></ul></li></ul></div>
+
+
+
+
+
+
+ <div id="introduction" class="section">
+ <!--OddPage--><h2><span class="secno">1. </span>Introduction<br>
+</h2>
+
+<p>
+Provenance is a record that describes the people, institutions, entities, and activities involved in producing, influencing, or delivering a piece of data or a thing.
+This document complements
+ the PROV-DM specification [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>] that defines a data model for
+ provenance on the Web. This document defines a form of validation for provenance. </p>
+
+
+
+ <div id="conventions" class="section">
+<h3><span class="secno">1.1 </span>Conventions</h3>
+
+
+
+<p>The key words "<em class="rfc2119" title="must">must</em>", "<em class="rfc2119" title="must not">must not</em>", "<em class="rfc2119" title="required">required</em>", "<em class="rfc2119" title="shall">shall</em>", "<em class="rfc2119" title="shall
+ not">shall
+ not</em>", "<em class="rfc2119" title="should">should</em>", "<em class="rfc2119" title="should not">should not</em>", "<em class="rfc2119" title="recommended">recommended</em>", "<em class="rfc2119" title="may">may</em>", and
+ "<em class="rfc2119" title="optional">optional</em>" in this document are to be interpreted as described in
+ [<cite><a class="bibref" rel="biblioentry" href="#bib-RFC2119">RFC2119</a></cite>].</p>
+
+<p>In this document, logical formulas contain variables written as
+ lower-case identifiers. Some of these variables are written
+ beginning with the underscore character <span class="name">_</span>, by convention, to indicate that they
+ appear only once in the formula. Such variables are
+ provided merely as an aid to the reader. </p>
+
+</div>
+
+
+<div id="purpose" class="section">
+
+<h3><span class="secno">1.2 </span>Purpose of this document</h3>
+
+</div>
+
+<div id="structure-of-this-document" class="section">
+<h3><span class="secno">1.3 </span>Structure of this document</h3>
+<p>
+</p>
+
+
+
+</div>
+<div id="audience" class="section">
+<h3><span class="secno">1.4 </span> Audience </h3>
+
+
+<p>This document assumes familiarity with [<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-DM">PROV-DM</a></cite>] and employs the
+[<cite><a class="bibref" rel="biblioentry" href="#bib-PROV-N">PROV-N</a></cite>] notation.
+</p>
+
+</div>
+</div>
+
+<div id="test" class="section">
+<!--OddPage--><h2><span class="secno">2. </span>MathJax test</h2>
+
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-1-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-1"><span style="display: inline-block; position: relative; width: 0px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(74px 19360px 80px -9px); top: -77px; left: 0px;"><span class="mrow" id="MathJax-Span-2"></span><span style="display: inline-block; width: 0px; height: 77px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 2px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-1">\newcommand{\wasDerivedFrom}{\mathit{wasDerivedFrom}}</script>
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-2-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-3"><span style="display: inline-block; position: relative; width: 0px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(74px 19360px 80px -9px); top: -77px; left: 0px;"><span class="mrow" id="MathJax-Span-4"></span><span style="display: inline-block; width: 0px; height: 77px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 2px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-2">\newcommand{\wasInformedBy}{\mathit{wasInformedBy}}</script>
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-3-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5"><span style="display: inline-block; position: relative; width: 0px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(74px 19360px 80px -9px); top: -77px; left: 0px;"><span class="mrow" id="MathJax-Span-6"></span><span style="display: inline-block; width: 0px; height: 77px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 2px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-3">\newcommand{\wasGeneratedBy}{\mathit{wasGeneratedBy}}</script>
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-4-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7"><span style="display: inline-block; position: relative; width: 0px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(74px 19360px 80px -9px); top: -77px; left: 0px;"><span class="mrow" id="MathJax-Span-8"></span><span style="display: inline-block; width: 0px; height: 77px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 2px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-4">\newcommand{\used}{\mathit{used}}</script>
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-5-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9"><span style="display: inline-block; position: relative; width: 0px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(74px 19360px 80px -9px); top: -77px; left: 0px;"><span class="mrow" id="MathJax-Span-10"></span><span style="display: inline-block; width: 0px; height: 77px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 2px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-5">\newcommand{\entity}{\mathit{entity}}</script>
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-6-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11"><span style="display: inline-block; position: relative; width: 0px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(74px 19360px 80px -9px); top: -77px; left: 0px;"><span class="mrow" id="MathJax-Span-12"></span><span style="display: inline-block; width: 0px; height: 77px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 2px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-6">\newcommand{\activity}{\mathit{activity}}</script>
+
+<p>When <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-7-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-13"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-14"><span class="mi" id="MathJax-Span-15" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-16" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≠</span><span class="mn" id="MathJax-Span-17" style="font-family: STIXGeneral-Regular; padding-left: 6px;">0</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.1px; vertical-align: -4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-7">a \ne 0</script>, there are two solutions to <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-8-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-18"><span style="display: inline-block; position: relative; width: 132px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(28.7px 19360px 51.8px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-19"><span class="mi" id="MathJax-Span-20" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-21"><span style="display: inline-block; position: relative; width: 18.4px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -9.5px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-22" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49px; left: 10px;"><span class="mn" id="MathJax-Span-23" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-24" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">+</span><span class="mi" id="MathJax-Span-25" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">b</span><span class="mi" id="MathJax-Span-26" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-27" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">+</span><span class="mi" id="MathJax-Span-28" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">c</span><span class="mo" id="MathJax-Span-29" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mn" id="MathJax-Span-30" style="font-family: STIXGeneral-Regular; padding-left: 6px;">0</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -1.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-8">ax^2 + bx + c = 0</script> and they are
+<span class="MathJax_Preview"></span><div class="MathJax_Display" role="textbox" aria-readonly="true" style="text-align: center;"><span class="MathJax" id="MathJax-Element-9-Frame" style=""><nobr><span class="math" id="MathJax-Span-31"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(11px 19360px 64.5px -9.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-32"><span class="mi" id="MathJax-Span-33" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-34" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="texatom" id="MathJax-Span-35" style="padding-left: 6px;"><span class="mrow" id="MathJax-Span-36"><span class="mfrac" id="MathJax-Span-37" style="padding-left: 2.3px; padding-right: 2.3px;"><span style="display: inline-block; position: relative; width: 130.3px; height: 0px;"><span style="position: absolute; clip: rect(24.1px 19360px 54.2px -7.8px); top: -61.1px; left: 50%; margin-left: -64px;"><span class="mrow" id="MathJax-Span-38"><span class="mo" id="MathJax-Span-39" style="font-family: STIXGeneral-Regular;">−</span><span class="mi" id="MathJax-Span-40" style="font-family: STIXGeneral-Italic;">b</span><span class="mo" id="MathJax-Span-41" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">±</span><span class="msqrt" id="MathJax-Span-42" style="padding-left: 4.8px;"><span style="display: inline-block; position: relative; width: 83.5px; height: 0px;"><span style="position: absolute; clip: rect(27.8px 19360px 51.2px -8.6px); top: -48px; left: 15px;"><span class="mrow" id="MathJax-Span-43"><span class="msubsup" id="MathJax-Span-44"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-45" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.9px; left: 10px;"><span class="mn" id="MathJax-Span-46" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-47" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">−</span><span class="mn" id="MathJax-Span-48" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">4</span><span class="mi" id="MathJax-Span-49" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-50" style="font-family: STIXGeneral-Italic;">c</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(58.1px 19360px 65.1px -9px); top: -82px; left: 15px;"><span style="display: inline-block; position: relative; width: 68.5px; height: 0px;"><span style="position: absolute; font-family: STIXGeneral-Regular; top: -77px; left: 0px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="position: absolute; font-family: STIXGeneral-Regular; top: -77px; left: 58.8px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="font-family: STIXGeneral-Regular; position: absolute; top: -77px; left: 8px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="font-family: STIXGeneral-Regular; position: absolute; top: -77px; left: 16.5px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="font-family: STIXGeneral-Regular; position: absolute; top: -77px; left: 24.9px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="font-family: STIXGeneral-Regular; position: absolute; top: -77px; left: 33.4px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="font-family: STIXGeneral-Regular; position: absolute; top: -77px; left: 41.9px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="font-family: STIXGeneral-Regular; position: absolute; top: -77px; left: 50.3px;">‾<span style="display: inline-block; width: 0px; height: 77px;"></span></span></span><span style="display: inline-block; width: 0px; height: 77px;"></span></span><span style="position: absolute; clip: rect(55.2px 19360px 85px -6.8px); top: -78.8px; left: 0px;"><span style="font-family: STIXGeneral-Regular;">√</span><span style="display: inline-block; width: 0px; height: 77px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.9px 19360px 51.2px -8.4px); top: -34.7px; left: 50%; margin-left: -10px;"><span class="mrow" id="MathJax-Span-51"><span class="mn" id="MathJax-Span-52" style="font-family: STIXGeneral-Regular;">2</span><span class="mi" id="MathJax-Span-53" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(16.8px 19360px 24px -9px); top: -25.3px; left: 0px;"><span style="border-left-width: 130.3px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 1.25px; vertical-align: 0px;"></span><span style="display: inline-block; width: 0px; height: 21px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-54" style="font-family: STIXGeneral-Regular;">.</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 49.5px; vertical-align: -14.5px;"></span></span></nobr></span></div><script type="math/tex; mode=display" id="MathJax-Element-9">x = {-b \pm \sqrt{b^2-4ac} \over 2a}.</script>
+</p>
+
+<div class="inference" id="communication-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#communication-generation-use-inference">Inference 1 (communication-generation-use-inference)</a></div>
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-10-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-55"><span style="display: inline-block; position: relative; width: 993px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-56"><span class="mi" id="MathJax-Span-57" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-58" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-59" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-60" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-61" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-62" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-63" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-64" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-65" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-66" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-67" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-68" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-69" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-70" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-71" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-72" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-73" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-74" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-75" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;"> </span><span class="texatom" id="MathJax-Span-76"><span class="mrow" id="MathJax-Span-77"><span class="mi" id="MathJax-Span-78" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-79" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-80" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-81" style="font-family: STIXGeneral-Italic;">I</span><span class="mi" id="MathJax-Span-82" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-83" style="font-family: STIXGeneral-Italic;">f</span><span class="mi" id="MathJax-Span-84" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-85" style="font-family: STIXGeneral-Italic;">r</span><span class="mi" id="MathJax-Span-86" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-87" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-88" style="font-family: STIXGeneral-Italic;">d</span><span class="mi" id="MathJax-Span-89" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-90" style="font-family: STIXGeneral-Italic;">y</span></span></span><span class="mo" id="MathJax-Span-91" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-92" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-93" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-94" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-95" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-96" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-97" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-98" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-99" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-100" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-101" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-102" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-103" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-104" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-105" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-106" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-107" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-108" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-109" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⟹</span><span class="mi" id="MathJax-Span-110" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-111" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-112" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-113" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-114" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-115" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-116" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-117" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-118" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-119" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-120" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-121" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-122" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-123" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-124" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-125" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-126" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-127" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-128" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-129" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;"> </span><span class="texatom" id="MathJax-Span-130"><span class="mrow" id="MathJax-Span-131"><span class="mi" id="MathJax-Span-132" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-133" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-134" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-135" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-136" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-137" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-138" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-139" style="font-family: STIXGeneral-Italic;">r</span><span class="mi" id="MathJax-Span-140" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-141" style="font-family: STIXGeneral-Italic;">t</span><span class="mi" id="MathJax-Span-142" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-143" style="font-family: STIXGeneral-Italic;">d</span><span class="mi" id="MathJax-Span-144" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-145" style="font-family: STIXGeneral-Italic;">y</span></span></span><span class="mo" id="MathJax-Span-146" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-147" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-148" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-149" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-150" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-151" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-152" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-153" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-154" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-155" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-156" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-157" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-158" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-159" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-160" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-161" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-162" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-163" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-164" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="texatom" id="MathJax-Span-165" style="padding-left: 4.8px;"><span class="mrow" id="MathJax-Span-166"><span class="mi" id="MathJax-Span-167" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-168" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-169" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-170" style="font-family: STIXGeneral-Italic;">d</span></span></span><span class="mo" id="MathJax-Span-171" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-172" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-173" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-174" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-175" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-176" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-177" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-178" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-179" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-180" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-181" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-182" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-183" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-184" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-185" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-186" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-187" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-188" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-10">\forall id,a_2,a_1,attrs.~ \wasInformedBy(id,a_2,a_1,attrs) \Longrightarrow \exists e,gen,t_1,use,t_2.~\wasGeneratedBy(gen,e,a_1,t_1,[]) \wedge \used(use,a_2,e,t_2,[])</script></div>
+
+</div>
+
+
+<div id="inferences" class="section">
+<!--OddPage--><h2><span class="secno">3. </span>Inferences</h2>
+
+<div class="inference" id="communication-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#communication-generation-use-inference">Inference 2 (communication-generation-use-inference)</a></div><span class="math">∀ id,a<sub>2</sub>,a<sub>1</sub>,attrs. wasInformedBy(id,a<sub>2</sub>,a<sub>1</sub>,attrs) ⟹ ∃ e,gen,t<sub>1</sub>,use,t<sub>2</sub>. wasGeneratedBy(gen,e,a<sub>1</sub>,t<sub>1</sub>,[]) ∧ used(use,a<sub>2</sub>,e,t<sub>2</sub>,[])</span></div>
+<div class="inference" id="generation-use-communication-inference"><div class="ruleTitle"><a class="internalDFN" href="#generation-use-communication-inference">Inference 3 (generation-use-communication-inference)</a></div><span class="math">∀ gen,a<sub>1</sub>,t<sub>1</sub>,attrs<sub>1</sub>,id<sub>2</sub>,a<sub>2</sub>,t<sub>2</sub>,attrs<sub>2</sub>. wasGeneratedBy(gen,e,a<sub>1</sub>,t<sub>1</sub>,attrs<sub>1</sub>) ∧ used(id<sub>2</sub>,a<sub>2</sub>,e,t<sub>2</sub>,attrs<sub>2</sub>) ⟹ ∃ id. wasInformedBy(id,a<sub>2</sub>,a<sub>1</sub>,[])</span></div>
+<div class="inference" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a class="internalDFN" href="#entity-generation-invalidation-inference">Inference 4 (entity-generation-invalidation-inference)</a></div><span class="math">∀ gen,e,a<sub>1</sub>,t<sub>1</sub>,attrs<sub>1</sub>,id<sub>2</sub>,a<sub>2</sub>,t<sub>2</sub>,attrs<sub>2</sub>. wasGeneratedBy(gen,e,a<sub>1</sub>,t<sub>1</sub>,attrs<sub>1</sub>) ∧ used(id<sub>2</sub>,a<sub>2</sub>,e,t<sub>2</sub>,attrs<sub>2</sub>) ⟹ ∃ id. wasInformedBy(id,a<sub>2</sub>,a<sub>1</sub>,[])</span></div>
+<div class="inference" id="activity-start-end-inference"><div class="ruleTitle"><a class="internalDFN" href="#activity-start-end-inference">Inference 5 (activity-start-end-inference)</a></div><span class="math">∀ a,t<sub>1</sub>,t<sub>2</sub>,attrs. activity(a,t<sub>1</sub>,t<sub>2</sub>,attrs) ⟹ ∃ start,e<sub>1</sub>,a<sub>1</sub>,end,a<sub>2</sub>,e<sub>2</sub>. wasStartedBy(start,a,e<sub>1</sub>,a<sub>1</sub>,t<sub>1</sub>,[]) ∧ wasEndedBy(end,a,e<sub>2</sub>,a<sub>2</sub>,t<sub>2</sub>,[])</span></div>
+<div class="inference" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 6 (wasStartedBy-inference)</a></div><span class="math">∀ id,a,e<sub>1</sub>,a<sub>1</sub>,t,attrs. wasStartedBy(id,a,e<sub>1</sub>,a<sub>1</sub>,t,attrs) ⟹ ∃ gen,t<sub>1</sub>. wasGeneratedBy(gen,e<sub>1</sub>,a<sub>1</sub>,t<sub>1</sub>,[])</span></div>
+<div class="inference" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 7 (wasEndedBy-inference)</a></div><span class="math">∀ id,a,e<sub>1</sub>,a<sub>1</sub>,t,attrs. wasEndedBy(id,a,e<sub>1</sub>,a<sub>1</sub>,t,attrs) ⟹ ∃ gen,t<sub>1</sub>. wasGeneratedBy(gen,e<sub>1</sub>,a<sub>1</sub>,t<sub>1</sub>,[])</span></div>
+<div class="inference" id="derivation-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-use-inference">Inference 8 (derivation-generation-use-inference)</a></div>In this inference, none of <em>a</em>, <em>gen<sub>2</sub></em> or <em>use_1</em> can be placeholders -.<span class="math">∀ id,e<sub>2</sub>,e<sub>1</sub>,a,gen<sub>2</sub>,use<sub>1</sub>,attrs. wasDerivedFrom(id,e<sub>2</sub>,e<sub>1</sub>,a,gen<sub>2</sub>,use<sub>1</sub>,attrs) ⟹ ∃ s,t<sub>1</sub>,t<sub>2</sub>. used(use<sub>1</sub>,a,e<sub>1</sub>,t<sub>1</sub>,[]) ∧ wasGeneratedBy(gen<sub>2</sub>,e<sub>2</sub>,a,t<sub>2</sub>,[])</span></div>
+<div class="inference" id="revision-is-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#revision-is-alternate-inference">Inference 9 (revision-is-alternate-inference)</a></div>In this inference, any of <em>a</em>, <em>g</em> or <em>u</em> may be placeholders.<span class="math">∀ id,e<sub>1</sub>,e<sub>2</sub>,a,g,u. wasDerivedFrom(id,e<sub>2</sub>,e<sub>1</sub>,a,g,u,.(prov:type = prov:Revision,[])) ⟹ alternateOf(e<sub>2</sub>,e<sub>1</sub>)</span></div>
+<div class="inference" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 10 (attribution-inference)</a></div><span class="math">∀ att,e,ag,attrs. wasAttributedTo(att,e,ag,attrs) ⟹ ∃ a,t,gen,assoc,pl. wasGeneratedBy(gen,e,a,t,[]) ∧ wasAssociatedWith(assoc,a,ag,pl,[])</span></div>
+<div class="inference" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 11 (delegation-inference)</a></div><span class="math">∀ id,ag<sub>1</sub>,ag<sub>2</sub>,a,attrs. actedOnBehalfOf(id,ag<sub>1</sub>,ag<sub>2</sub>,a,attrs) ⟹ ∃ id<sub>1</sub>,pl<sub>1</sub>,id<sub>2</sub>,pl<sub>2</sub>. wasAssociatedWith(id<sub>1</sub>,a,ag<sub>1</sub>,pl<sub>1</sub>,[]) ∧ wasAssociatedWith(id<sub>2</sub>,a,ag<sub>2</sub>,pl<sub>2</sub>,[])</span></div>
+<div class="inference" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 12 (influence-inference)</a></div><ol><li><span class="math">∀ id,e,a,t,attrs. wasGeneratedBy(id,e,a,t,attrs) ⟹ wasInfluencedBy(id,e,a,attrs)</span></li><li><span class="math">∀ id,a,e,t,attrs. used(id,a,e,t,attrs) ⟹ wasInfluencedBy(id,a,e,attrs)</span></li><li><span class="math">∀ id,a<sub>2</sub>,a<sub>1</sub>,attrs. wasInformedBy(id,a<sub>2</sub>,a<sub>1</sub>,attrs) ⟹ wasInfluencedBy(id,a<sub>2</sub>,a<sub>1</sub>,attrs)</span></li><li><span class="math">∀ id,a<sub>2</sub>,e,a<sub>1</sub>,t,attrs. wasStartedBy(id,a<sub>2</sub>,e,a<sub>1</sub>,t,attrs) ⟹ wasInfluencedBy(id,a<sub>2</sub>,e,attrs)</span></li><li><span class="math">∀ id,a<sub>2</sub>,e,a<sub>1</sub>,t,attrs. wasEndedBy(id,a<sub>2</sub>,e,a<sub>1</sub>,t,attrs) ⟹ wasInfluencedBy(id,a<sub>2</sub>,e,attrs)</span></li><li><span class="math">∀ id,e,a,t,attrs. wasInvalidatedBy(id,e,a,t,attrs) ⟹ wasInfluencedBy(id,e,a,attrs)</span></li><li><span class="math">∀ id,e<sub>2</sub>,e<sub>1</sub>,a,g,u,attrs. wasDerivedFrom(id,e<sub>2</sub>,e<sub>1</sub>,a,g,u,attrs) ⟹ wasInfluencedBy(id,e<sub>2</sub>,e<sub>1</sub>,attrs)</span></li><li>In this rule, <em>a</em>, <em>g</em>, <em>u</em> may be placeholders -.<span class="math">∀ id,e,ag,attrs. wasAttributedTo(id,e,ag,attrs) ⟹ wasInfluencedBy(id,e,ag,attrs)</span></li><li>In this rule, <em>pl</em> may be a placeholder -.<span class="math">∀ id,a,ag,pl,attrs. wasAssociatedWith(id,a,ag,pl,attrs) ⟹ wasInfluencedBy(id,a,ag,attrs)</span></li><li><span class="math">∀ id,ag<sub>2</sub>,ag<sub>1</sub>,a,attrs. actedOnBehalfOf(id,ag<sub>2</sub>,ag<sub>1</sub>,a,attrs) ⟹ wasInfluencedBy(id,ag<sub>2</sub>,ag<sub>1</sub>,attrs)</span></li></ol></div>
+<div class="inference" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 13 (alternate-reflexive)</a></div><span class="math">∀ e. entity(e) ⟹ alternateOf(e,e)</span></div>
+<div class="inference" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 14 (alternate-transitive)</a></div><span class="math">∀ e<sub>1</sub>,e<sub>2</sub>,e<sub>3</sub>. alternateOf(e<sub>1</sub>,e<sub>2</sub>) ∧ alternateOf(e<sub>2</sub>,e<sub>3</sub>) ⟹ alternateOf(e<sub>1</sub>,e<sub>3</sub>)</span></div>
+<div class="inference" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 15 (alternate-symmetric)</a></div><span class="math">∀ e<sub>1</sub>,e<sub>2</sub>. alternateOf(e<sub>1</sub>,e<sub>2</sub>) ⟹ alternateOf(e<sub>2</sub>,e<sub>1</sub>)</span></div>
+<div class="inference" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 16 (specialization-transitive)</a></div><span class="math">∀ e<sub>1</sub>,e<sub>2</sub>,e<sub>3</sub>. specializationOf(e<sub>1</sub>,e<sub>2</sub>) ∧ specializationOf(e<sub>2</sub>,e<sub>3</sub>) ⟹ specializationOf(e<sub>1</sub>,e<sub>3</sub>)</span></div>
+<div class="inference" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 17 (specialization-alternate-inference)</a></div><span class="math">∀ e<sub>1</sub>,e<sub>2</sub>. specializationOf(e<sub>1</sub>,e<sub>2</sub>) ⟹ alternateOf(e<sub>1</sub>,e<sub>2</sub>)</span></div>
+<div class="inference" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 18 (specialization-attributes-inference)</a></div><span class="math">∀ e<sub>1</sub>,attrs,e<sub>2</sub>. entity(e<sub>1</sub>,attrs) ∧ specializationOf(e<sub>2</sub>,e<sub>1</sub>) ⟹ entity(e<sub>2</sub>,attrs)</span></div>
+<div class="constraint" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint 19 (membership-empty-collection)</a></div><span class="math">∀ c,e. hasMember(c,e) ∧ prov:EmptyCollection \in typeOf(c) ⟹ False</span></div>
+
+</div>
+
+<div class="appendix section" id="acknowledgements">
+ <!--OddPage--><h2><span class="secno">A. </span>Acknowledgements</h2>
+ <p>
+
+This document has been produced by the PROV Working Group, and its contents reflect extensive discussion within the Working Group as a whole. The editors extend special thanks to Ivan Herman (<acronym title="World Wide Web Consortium">W3C</acronym>/<acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym>), Paul Groth, Tim Lebo, Simon Miles, Stian Soiland-Reyes, for their thorough reviews.
+ </p>
+
+<p>
+Members of the PROV Working Group at the time of publication of this document were:
+
+Ilkay Altintas (Invited expert),
+Reza B'Far (Oracle Corporation),
+Khalid Belhajjame (University of Manchester),
+James Cheney (University of Edinburgh, School of Informatics),
+Sam Coppens (IBBT),
+David Corsar (University of Aberdeen, Computing Science),
+Stephen Cresswell (The National Archives),
+Tom De Nies (IBBT),
+Helena Deus (DERI Galway at the National University of Ireland, Galway, Ireland),
+Simon Dobson (Invited expert),
+Martin Doerr (Foundation for Research and Technology - Hellas(FORTH)),
+Kai Eckert (Invited expert),
+Jean-Pierre EVAIN (European Broadcasting Union, EBU-UER),
+James Frew (Invited expert),
+Irini Fundulaki (Foundation for Research and Technology - Hellas(FORTH)),
+Daniel Garijo (Universidad Politécnica de Madrid),
+Yolanda Gil (Invited expert),
+Ryan Golden (Oracle Corporation),
+Paul Groth (Vrije Universiteit),
+Olaf Hartig (Invited expert),
+David Hau (National Cancer Institute, NCI),
+Sandro Hawke (<acronym title="World Wide Web Consortium">W3C</acronym>/<acronym title="Massachusetts Institute of Technology">MIT</acronym>),
+Jörn Hees (German Research Center for Artificial Intelligence (DFKI) Gmbh),
+Ivan Herman, (<acronym title="World Wide Web Consortium">W3C</acronym>/<acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym>),
+Ralph Hodgson (TopQuadrant),
+Hook Hua (Invited expert),
+Trung Dong Huynh (University of Southampton),
+Graham Klyne (University of Oxford),
+Michael Lang (Revelytix, Inc.),
+Timothy Lebo (Rensselaer Polytechnic Institute),
+James McCusker (Rensselaer Polytechnic Institute),
+Deborah McGuinness (Rensselaer Polytechnic Institute),
+Simon Miles (Invited expert),
+Paolo Missier (School of Computing Science, Newcastle university),
+Luc Moreau (University of Southampton),
+James Myers (Rensselaer Polytechnic Institute),
+Vinh Nguyen (Wright State University),
+Edoardo Pignotti (University of Aberdeen, Computing Science),
+Paulo da Silva Pinheiro (Rensselaer Polytechnic Institute),
+Carl Reed (Open Geospatial Consortium),
+Adam Retter (Invited Expert),
+Christine Runnegar (Invited expert),
+Satya Sahoo (Invited expert),
+David Schaengold (Revelytix, Inc.),
+Daniel Schutzer (FSTC, Financial Services Technology Consortium),
+Yogesh Simmhan (Invited expert),
+Stian Soiland-Reyes (University of Manchester),
+Eric Stephan (Pacific Northwest National Laboratory),
+Linda Stewart (The National Archives),
+Ed Summers (Library of Congress),
+Maria Theodoridou (Foundation for Research and Technology - Hellas(FORTH)),
+Ted Thibodeau (OpenLink Software Inc.),
+Curt Tilmes (National Aeronautics and Space Administration),
+Craig Trim (IBM Corporation),
+Stephan Zednik (Rensselaer Polytechnic Institute),
+Jun Zhao (University of Oxford),
+Yuting Zhao (University of Aberdeen, Computing Science).
+</p>
+ </div>
+
+
+
+<!-- LocalWords: px DM RL RDF AQ SEM SOTD Definitional wasInformedBy attrs ag
+ -->
+<!-- LocalWords: wasGeneratedBy wasStartedBy gAttr sAttr wasAttributedTo attr
+ -->
+<!-- LocalWords: wasAssociatedWith dAttrs gAttrs wasDerivedFrom uAttrs eAttrs
+ -->
+<!-- LocalWords: wasRevisionOf specializationOf wasQuotedFrom Traceability WD
+ -->
+<!-- LocalWords: tracedTo aAttr actedOnBehalfOf rAttr traceability TODO xsd
+ -->
+<!-- LocalWords: alternateOf wasEndedBy Lamport's timeline subfigure memberOf
+ -->
+<!-- LocalWords: wasStartedByAgent wasAttributedWith derivedByInsertionFrom
+ -->
+<!-- LocalWords: QName derivedByRemovalFrom EmptyCollection wasVersionOf dm
+ -->
+<!-- LocalWords: RecsWD formedness workflow ness operability CSP versa hyp YY
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+<!-- LocalWords: disambiguating lifecycle conformant minimalistic Lamport fo
+ -->
+<!-- LocalWords: reflexivity antisymmetry timelines timespan WG concl inv TBD
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+<!-- LocalWords: customerInChairAt manWithGlasses customerInChair irreflexive
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+ -->
+<!-- LocalWords: DBCONSTRAINTS formalisms URIs wasInfluencedBy definitional
+ -->
+<!-- LocalWords: wasInvalidated th nontermination implementability att evt
+ -->
+<!-- LocalWords: Irreflexivity mentionOf preorder equalities unsatisfiable De
+ -->
+<!-- LocalWords: Lebo subfigures pre del irreflexivity superproperty typeOf
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+ -->
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+ -->
+<!-- LocalWords: implementers multi unifier ERCIM Groth Stian Soiland Ilkay
+ -->
+<!-- LocalWords: Altintas Reza B'Far Belhajjame Informatics Coppens IBBT Nies
+ -->
+<!-- LocalWords: Corsar Cresswell Deus DERI Galway satisfiable namespace Kai
+ -->
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+ -->
+<!-- LocalWords: Pignotti Paulo Pinheiro Geospatial Retter Runnegar Satya
+ -->
+<!-- LocalWords: Sahoo Schaengold Schutzer FSTC Yogesh Simmhan Theodoridou
+ -->
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+<div id="MathJax_Font_Test" style="position: absolute; visibility: hidden; top: 0px; left: 0px; width: auto; padding: 0px; border: 0px; margin: 0px; white-space: nowrap; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; font-size: 40px; font-weight: normal; font-style: normal; font-family: STIXSizeOneSym, sans-serif;">() {} []</div><div id="references" class="appendix section"><!--OddPage--><h2><span class="secno">B. </span>References</h2><div id="normative-references" class="section"><h3><span class="secno">B.1 </span>Normative references</h3><dl class="bibliography"><dt id="bib-PROV-DM">[PROV-DM]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/"><cite>PROV-DM: The PROV Data Model</cite></a>. 11 December 2012, W3C Candidate Recommendation. URL: <a href="http://www.w3.org/TR/2012/CR-prov-dm-20121211/">http://www.w3.org/TR/2012/CR-prov-dm-20121211/</a>
+</dd><dt id="bib-PROV-N">[PROV-N]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/"><cite>PROV-N: The Provenance Notation</cite></a>. 11 December 2012, W3C Candidate Recommendation. URL: <a href="http://www.w3.org/TR/2012/CR-prov-n-20121211/">http://www.w3.org/TR/2012/CR-prov-n-20121211/</a>
+</dd><dt id="bib-PROV-O">[PROV-O]</dt><dd>Timothy Lebo; Satya Sahoo; Deborah McGuinness; eds. <a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/"><cite>PROV-O: The PROV Ontology</cite></a>. 11 December 2012, W3C Candidate Recommendation. URL: <a href="http://www.w3.org/TR/2012/CR-prov-o-20121211/">http://www.w3.org/TR/2012/CR-prov-o-20121211/</a>
+</dd><dt id="bib-RFC2119">[RFC2119]</dt><dd>S. Bradner. <a href="http://www.ietf.org/rfc/rfc2119.txt"><cite>Key words for use in RFCs to Indicate Requirement Levels.</cite></a> March 1997. Internet RFC 2119. URL: <a href="http://www.ietf.org/rfc/rfc2119.txt">http://www.ietf.org/rfc/rfc2119.txt</a>
+</dd></dl></div><div id="informative-references" class="section"><h3><span class="secno">B.2 </span>Informative references</h3><dl class="bibliography"><dt id="bib-PROV-AQ">[PROV-AQ]</dt><dd>Graham Klyne; Paul Groth; eds. <a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/"><cite>Provenance Access and Query</cite></a>. 19 June 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-aq-20120619/">http://www.w3.org/TR/2012/WD-prov-aq-20120619/</a>
+</dd><dt id="bib-PROV-OVERVIEW">[PROV-OVERVIEW]</dt><dd>Paul Groth; Luc Moreau; eds. <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/"><cite>PROV-OVERVIEW: An Overview of the PROV Family of Documents</cite></a>. 11 December 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-overview-20121211/">http://www.w3.org/TR/2012/WD-prov-overview-20121211/</a>
+</dd><dt id="bib-PROV-PRIMER">[PROV-PRIMER]</dt><dd>Yolanda Gil; Simon Miles; eds. <a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/"><cite>PROV Model Primer</cite></a>. 11 December 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-primer-20121211/">http://www.w3.org/TR/2012/WD-prov-primer-20121211/</a>
+</dd><dt id="bib-PROV-XML">[PROV-XML]</dt><dd>Hook Hua; Curt Tilmes; Stephan Zednik; eds. <a href="http://www.w3.org/TR/2012/WD-prov-xml-20121211/"><cite>PROV-XML: The PROV XML Schema</cite></a>. 11 December 2012, Working Draft. URL: <a href="http://www.w3.org/TR/2012/WD-prov-xml-20121211/">http://www.w3.org/TR/2012/WD-prov-xml-20121211/</a>
+</dd></dl></div></div></body></html>
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